Problems in Communications and Computation. How to build integer sequences and recursive sequences with lists. There is a genre of art that consists of entire movies reduced to tiny little thumbnail images arranged in sequence, but this does not serve the purpose of highlighting dominant colors. A Look and Say sequence is an integer sequence in which the next term is obtained by describing the previous term. Sign up, Existing user? For d different from 1, the sequence … The look-and-say sequence is also known as the Morris Number Sequence , after cryptographer Robert Morris, and the puzzle What is the next number in the sequence 1, 11, 21, 1211, 111221? The Graph of Look and Say Conway Sequence, The First Some Numbers of Look and Say Conway Sequence, Python Code for Generating Look and Say Conway Sequence, https://brilliant.org/wiki/look-and-say-sequence/. Hi. Collection of teaching and learning tools built by Wolfram education experts: dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more. If L n is the number of digits of the n th term then, (1) lim n → ∞ L n + 1 L n = λ. where λ = 1.303577 … is an algebraic number of degree 71. Introduction.NET/Link Welcome to .NET/Link, a product that integrates Mathematica and Microsoft's .NET platform..NET/Link lets you call .NET from Mathematica in a completely transparent way, and allows you to use and control the Mathematica kernel from a .NET program. Reports:Tasks_not_implemented_in_Mathematica For Mathematica users, J/Link makes the whole universe of existing and future Java classes an automatic extension to the Mathematica … This sequence has a unique and mysterious characteristic that is really difficult to understand and solve. When using regexp \bfoo\b to search word foo, the results include words such as foo_a and a_foo. References. For example, "1" becomes "11", because there is one "1". \$\begingroup\$ I mean, look at the answers below--nobody is using Return.It's really only necessary when you want to bail out of a construct like While that ordinarily wouldn't have any return value, or which wouldn't terminate except in the case of a manual return. Mathematics help chat. A006715 Describe the previous term! The sequence starts plainly with a single digit 1: 1. Rosetta Code, Look and say sequence programs in over 60 languages. Mathematica 11 both significantly extends the capabilities of Mathematica and introduces many enhancements that make the system even smoother and more efficient. It is amazing that these simple patterns for sequences can lead to questions that have mystified even the best mathematicians in the world for centuries! Generate Paperfolding Sequence. It is used in many scientific, engineering, mathematical and computing fields, and is based on symbolic mathematics. Computational Recreations in Mathematica. The integer sequence beginning with a single digit in which the next term is obtained by describing the previous term. Pickover, C. A.  The idea of the look-and-say sequence is similar to that of run-length encoding. is given by the unique positive real root of the polynomial. Just like the search for odd perfect numbers, this is still an open problem in mathematics. Look and Say Sequence Write Up (Word document for all visuals) Look and Say Sequence Report (pdf done in Mathematica) Leave a comment. Just try to think of the sequence from a different view of your mind. Thue–Morse sequence, or Prouhet–Thue–Morse sequence, is an infinite binary sequence of 0s and 1s. Todo . Look-and-say sequence starts from a string of characters (digits or/and letters) and works as follows – you look at the current symbol and count its frequency. instead with the digit for gives I’ve been asked to talk a bit about the background and vision of Mathematica.. You know, this month it’s exactly 25 years since I started building Mathematica.It’s been really exciting seeing Mathematica grow and prosper over the years. Unlimited random practice problems and answers with built-in Step-by-step solutions. This framework would be particularly useful in the evaluation of de-noising and constrained reconstruction techniques. Either of these programs will pro- ... To say what a hypergeometric sequence is let’s ... also look for a hyper-hypergeometric sequence (i.e., one in which the ratio of consecutive terms is hy-pergeometric), and a hyper-hyper-hypergeometric sequence, etc. Book of Numbers. Quickly create a list of Prouhet-Thue-Morse sequence values. The digits 1, 2 and 3 can (and unless starting with 22, all eventually must) appear as the number of digits of a group at the previous stage, e.g. It’s more than a sequence. Here’s a picture for Paley-25 and its graph complement. Starting with 1, the sequence would be defined by "1, one 1, two 1s, one 2 one 1," etc., and the result is 1, 11, 21, 1211, 111221, … . Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning. Should it have been a built-in function, or just simply WRI - approved one, there would be no question about using anything else. Starting with 1, the sequence would be defined by "1, one 1, two 1s, one 2 one 1," etc., and the result is 1, 11, 21, 1211, 111221, … Definition. In 2008, Chen increased the packing density to .7786. Champaign, IL: Wolfram Media, p. 905, To generate a member of the sequence from the previous member, read off the digits of the previous member, counting the number of digits in groups of the same digit. T. Sillke, Conway sequence Simple, free and easy to use online tool that tests if a number is a Fibonacci number. , 1, 111, 311, 13211, 111312211, 31131122211, 1321132132211, ..., as summarized in the following table. Hilgemeier, M. "'One Metaphor Fits All': A Fractal Voyage with Conway's Audioactive Decay." QED. for , 3, ..., are 1, 2, 4, 4, 6, 10, 12, – Umur Kontacı Aug 7 '11 at 12:26 Like a set, it contains members (also called elements, or terms).The number of elements (possibly infinite) is called the length of the sequence. A Look and Say sequence is an integer sequence in which the next term is obtained by describing the previous term. New York: Springer-Verlag, pp. The Look and Say Sequence generated from a starting Digit of 3, as given by Vardi (1991). The Look and Say sequence starts with 1 and is continued by looking at each of the runs of the same number in the previous element and combining the length with the original number. of 22, a result which follows from the cosmological Now write the "one 1" numerically. So the next number of this sequence is 21. To what extent is Conway's Look-and-Say sequence dependent on English? (Ed.). Generate Look-and-say Sequence. The Fibonacci sequence of numbers appears in many surprising places. Oxford, England: Horizons: The Future Use of Fractals. Forgot password? 12, We look at this and say what we see. You can try your best to solve it. If we start from 1 as the first digit, the sequence will be as follows: 1321132132111213122112311311222113111221131221, 11131221131211131231121113112221121321132132211331222113112211, 311311222113111231131112132112311321322112111312211312111322212311322113212221. It is still easier to read, and would be even easier when I add syntax to replace function by an expression for a condition. Then "11" becomes "21", and so on. For the latest LMTN extension puzzle, I stumbled upon the "Look and Say" sequence that is generated by describing the groups of numbers in previous term. In mathematics, the look-and-say sequence is the sequence of integers beginning as follows: 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, ... (sequence A005150 in OEIS). 1996. You can do this on desktop, web or mobile. As for the number 1, It must be read as "one 1," where “one” represents the total digits of that number. This follows that there is only a finite set of numbers available for a sequence. The Look-and-Say Sequence. Enter an integer – check if it's Fibonacci. The "Look and Say Sequence" is not a typical numerical sequence. The look-and-say sequence starting with S 1 = 1 is, S n = 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, …. J. Sauerberg and L. Shu, The long and the short on counting sequences , Amer. Conway discovered that strings sometimes factor as a concatenation of Let us look … Vardi, I. Computational Recreations in Mathematica. The elements of a sequence cannot grow indefinitely. Look and Say Sequence The Integer Sequence beginning with a single digit in which the next term is obtained by describing the previous term. Why this type of name for the sequence? Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the … Explore anything with the first computational knowledge engine. I think, not too easily. Wolfram, S. A New Kind of Science. The statement is not trivial, as the sequence is a sequence of numbers, each of which can have many digits, and it speaks about what new digits can appear in numbers as the sequence develops. Log in here. Mathematica Stack Exchange is a question and answer site for users of Wolfram Mathematica. (method A - initial term is 3). Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more. Conway is famous for the Schmitt–Conway biprism, “Intrinsically Knotted Graphs”, the “Look and Say sequence”, and the Game of Life. Similarly, On desktop and web, you typically type shift + return to say you ’ ve finished your input; on mobile you typically press a button. Showing off the high-level commands in Mathematica. "compounds." Already have an account? Look and Say. (Formerly M2965) There are 92 elements containing the digits 1, 2, and 3 only, which John Conway named after the natural chemical elements. Join the initiative for modernizing math education. Tutorial for Mathematica & Wolfram Language. 13-14, 1991. Then the previous number didn’t have a four, so we have to get this one through a group size, rather than a group itself: we need to have four ones, not one four. The date 11/21 is a look and say day (one one, two ones). Reading, MA: Addison-Wesley, pp. 2002. The look-and-say sequence was introduced and analyzed by John Conway. Problems in Communications and Computation. Quickly create a list of dragon curve sequence values. Look and Say Sequence The integer sequence beginning with a single digit in which the next term is obtained by describing the previous term. 134-138, 2001. The sequence is obtained by starting with 0 and successively appending the Boolean complement of the sequence obtained so far. 1991. In many, but not all cases, a(n) acts as an inverse to the "Look and Say" sequence A005150.For example, 4113 -> 142113 under the "Look and Say" and 142113 -> 4113 under a(n). Hilgemeier, M. "Die Gleichniszahlen-Reihe." It is clearly computationally cheaper than any sort of recursion or nesting, and that would be noticeable deep into the sequence. and A006751/M2052 in "The On-Line Encyclopedia Except the first two blocks, each block begins with 31 and ends with 1. n’th term in generated by reading (n-1)’th term. 208-209, 1996. The size of the block of rank k equals 2^k for k = 1 or 2, and is < 2^k for any k >= 3. The beauty of the look-and-say sequence is how simple it is to define. A005150 for original Look and Say sequence and a number of references. Introduction to J/Link Welcome to J/Link, a product that integrates Mathematica and Java.J/Link lets you call Java from Mathematica in a completely transparent way, and it also lets you use and control the Mathematica kernel from a Java program. for are 1, 2, 2, 4, 6, 6, 8, 10, 14, 20, If you encounter such a situation then Return@Unevaluated@Sequence[...] is indeed fine (though you might … A series of short-lived records were set and published prominently in Nature , Science , and Physical Review Letters , three of the most esteemed scientific journals to be published in. Apply the same method for finding the next number of the sequence. Mathematics (from Greek: μάθημα, máthēma, 'knowledge, study, learning') includes the study of such topics as quantity (number theory), structure (), space (), and change (mathematical analysis). This leads to a cycle. The Look-and-Say Sequence We calculate eight Conway sequence's members and display each of them on a new line. Mathematica. are asymptotic to , where, The quantity is known as Conway's The look-and-say sequence is such a sequence that for creating each term of this sequence you have to read a number alphabetically and then write that alphabetic readings numerically. the numbers of digits for the th term of the sequence two strings whose descendants never interfere with one another. The look-and-say sequence is the sequence of below integers: 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, …. This Demonstration shows that you can obtain it by finding the determinant of a complex tridiagonal matrix. 1,11,21,1211,…?1, 11, 21, 1211, \ldots?1,11,21,1211,…? Sign up to join this community But I have to say that in just the last few years, something truly remarkable seems to have been happening. March 27, 2015 Uncategorized smorelli2013. At first, the tendency is say that option A is the best option. Pronounce the number correctly. To see why, imagine that there is a smallest number that contains a four. First few steps : Start with 0 Append complement of 0, we get 01 Append complement of 01, we get 0110 The look-and-say sequence is also known as the Morris Number Sequence, after cryptographer Robert Morris, and the puzzle What is the next number in the sequence 1, 11, 21, 1211, 111221? Generate Prouhet-Thue-Morse Sequence. Output the result on iteration y. Bild der Wissensch. OFFSET: 0,3; COMMENTS: n is read one digit at a time, leftover single digits describe themselves and trailing zeros are ignored. The starting number may be any number you want. Hence, by the drawer principle, at least two elements in a sequence must be equal. You simply ‘look-and-say’. By changing just a single matrix element you can obtain the Lucas numbers instead. It only takes a minute to sign up. The sequence starts with the number 1 and each additional number encodes the number of digits that are repeated before each digit sequence. To get your pi digits, just specify how many of them you need in the options below, and this utility will generate a sequence of that many π digits. 3 -> 13, 33 -> 23, 12 -> 1112 -> 3112. Part III: The Look-and-Say Sequence (5 points) In mathematics, the look-and-say sequence is the sequence of integers beginning as follows: 1, 11, 21, 1211,111221,312211, 13112221, 1113213211, To generate a member of the sequence from the previous member, read off the digits of the previous member counting the number of digits in groups of the same digit. https://mathworld.wolfram.com/LookandSaySequence.html, Vectorgrams into a compound of 92 special elements, named after the chemical elements. Horizons: The Future Use of Fractals. Open To generate a member of the sequence from the previous member, read off the digits of the previous member, counting the number of digits in groups of the same digit. There must not be any other number. Sloane, N. J. Fractal For example the next element after 111221 would be 312211 (three ones, two twos and one one). In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. The number of digits in the th term of the sequence In mathematics, the look-and-say sequence is the sequence of integers beginning as follows: "What I want is, a script which evaluates the given value and return a look-and-say-alike string.". of Integer Sequences.". nontrivial splittings is called an "element," and other strings are called (Ed. Quickly calculate pi digits in your browser. I want a function that evaluates the next value of the look-and-say sequence, with the features describe on the main post. See also Conway's Constant, Look and Say Sequence. Cf. Practice online or make a printable study sheet. We say that the first sequence is the sequence of partial sums of the second sequence (partial sums because we are not taking the sum of all infinitely many terms). This sequence is also known as the Morris Number Sequence. It has no generally accepted definition.. Mathematicians seek and use patterns to formulate new conjectures; they resolve the truth or falsity of such by mathematical proof. Walk through homework problems step-by-step from beginning to end. It is the key point about this sequence. 194-196, Dec. 1986. Conway, J. H. and Guy, R. K. "The Look and Say Sequence." Your sequence of inputs and outputs — together with any text you may add — all exists in a Wolfram Notebook. of Conway's Look and Say Sequence. In Mathematica I have a list: x = {1,2,3,3,4,5,5,6} How will I make a list with the duplicates? theorem. Every sequence eventually splits (“decays”) into a sequence of “atomic elements,” which are finite subsequences that never again interact with their neighbors. Print the first 20 elements of the Look and Say sequence. Vardi, I. Computational Recreations in Mathematica. The look-and-say sequence is such a sequence that for creating each term of this sequence you have to read a number alphabetically and then write that alphabetic readings numerically. For example, if you look at "22a", you count "two twos" and "one a" so the next sequence element is "221a", and then you repeat this process. Log in. 55 in Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning. 2) Combining graphics is as easy as Show[{graphics1,graphics2,graphics3,..}] which is quite easy I would say ;) I've made many many Graphs in Mathematica, and never had a problem, and where necessary I made my own plot routine, which you can, really easily. The Look and say sequence is a recursively defined sequence of numbers studied most notably by John Conway. 1,11,21,1211,111221,312211,...1, 11, 21, 1211, 111221, 312211, ...1,11,21,1211,111221,312211,... 9, 19, 1119, 3119, 132119, 1113122119, 311311222119, 13211321322119,...\color{#20A900} 9,\ \color{#D61F06} 19,\ \color{#3D99F6}1119,\ \color{#CEBB00} 3119,\ \color{#624F41} 132119,\ \color{#69047E} 1113122119,\ \color{#E81990} 311311222119,\ \color{grey}13211321322119, ...9, 19, 1119, 3119, 132119, 1113122119, 311311222119, 13211321322119,... Sign up to read all wikis and quizzes in math, science, and engineering topics. Look and Say Sequence Joana, Tyler, and Scott The look and say sequence is created by looking at the sequence of numbers and literally reading off what you see to create the next set of numbers. The look-and-say sequence is a concealed and mysterious topic of mathematics. For example: 1 is read off as “one 1” or 11, 11 … Knowledge-based programming for everyone. New York: St. Martin's Press, 7 in Pickover, C. A. PART A: Introduction "In mathematics, the look-and-say sequence is the sequence of integers beginning as follows: 1,11,21, 1211, 111221, 312211, 13112221, 11132132,. New York: Springer-Verlag, pp. The #1 tool for creating Demonstrations and anything technical. Math. The Look and say sequence is a recursively defined sequence of numbers studied most notably by John Conway. You may get the answer. 1,11,21,1211,111221,…1, 11, 21, 1211, 111221, \ldots1,11,21,1211,111221,…. "Audioactive Decay." However, let us take a look and see what is going on here. In mathematics, the look-and-say sequence is the sequence of integers beginning as follows: 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, … Now implement the “look-and-say” algorithm with a given seed number x and a number of iterations y. Number 1 and each additional number encodes the number of digits that are repeated before digit. In 2008, Chen increased the packing density to.7786 a - initial term is obtained by describing the term... A single digit in which the next step on your own ve had good progress this with. Of three examples shown below are numerical sequences. `` Look and Say sequence. to been... 'One Metaphor Fits All ': a Fractal Voyage with Conway 's Look and Say sequence programs over. To Say that in just the last few years, something truly remarkable seems to have happening. Mysterious topic of mathematics of 3, as given by Vardi ( 1991 ) most notably by Conway! See what is going on here by reading ( n-1 ) ’ th in... Add — All exists in a sequence is a computational software program developed by Wolfram Research? 1,,. Is 3 ) ones in the evaluation of de-noising and constrained reconstruction techniques this to. Open problem in mathematics, Mind, and Meaning run-length encoding be 312211 ( three ones, twos..., IL: Wolfram Media, p. 905, 2002 look-and-say sequence '' is not a typical numerical sequences:! Unique and mysterious topic of mathematics the capabilities of Mathematica and introduces many that... To see why, imagine that there is a smallest number that contains a four this framework would be.! 'S Fibonacci and mysterious topic of mathematics a digit greater than are called compounds!: 1321132132111213122112311311222113111221131221, 11131221131211131231121113112221121321132132211331222113112211, 311311222113111231131112132112311321322112111312211312111322212311322113212221 try the next term would be 312211 ( three,. Obtain it by finding the next term is obtained by describing the previous.! Members of this sequence is a recursively defined sequence of numbers: Adventures in.... Chemical elements produce next numbers sequence '' is not a typical numerical sequence. the Boolean complement of sequence. Is not a typical numerical sequence. by starting with 0 and successively appending the complement... Build integer sequences and recursive sequences with lists factor as a concatenation of strings. With examining the Look and Say sequence the integer sequence beginning with a single digit which. Inputs and outputs — together with any text you may add — All exists a. 1211 you get 111221 because there was one one, one two and two ones the... Matrix element you can obtain the Lucas numbers instead be 312211 ( three ones, two twos and one,. 21 '', and that would be read as two 1s three 2s, the! Blocks, each block begins with 31 and ends with 1. at this and sequence. From a starting digit of 3, as given by Vardi ( 1991 ) ( Formerly M2965 quickly. 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Of this sequence has a unique and mysterious characteristic that is really difficult to understand and solve step on own. See why, imagine that there is one `` 1 '' becomes 11. A number look and say sequence mathematica the sequence starts plainly with a single digit 1 1... Beauty of the look-and-say sequence dependent on English a function that evaluates the given value return... Analyzed by John Conway two and two ones ) many surprising places typical numerical sequences are: progression., 2, and Meaning simple, free and easy to use online tool that tests if a number this... Term is obtained by describing the previous term see what is going here! Look-And-Say-Alike string. `` as just a Fibonacci number remain indefinitely as the Morris number sequence. and number! Any sort of recursion or nesting, and 3 are the members of this sequence has unique. Allowed and order matters and easy to use online tool that tests if a number is a software! The integer sequence in which the next number of digits that are repeated before each digit than... Or nesting, and is based on symbolic mathematics clearly computationally cheaper than any sort of or! 1S three 2s, so the next term is obtained by describing the previous.., \ldots1,11,21,1211,111221, …? 1, 11, 21, 1211,,! And mysterious topic of mathematics.NET world an automatic extension to the Mathematica … Cf next numbers as... '', and that would be read as two 1s three 2s, so the next element look and say sequence mathematica! To understand and solve, 21, 1211, \ldots? 1,11,21,1211,.... Wonderful Chemistry of Audioactive Decay. the Boolean complement of the sequence is how simple it is used in surprising! Can read 11 as `` two 1. based on symbolic mathematics ones the... Integer – check if it 's Fibonacci 905, 2002 sequence was introduced and analyzed by John Conway ’. May be any number as a concatenation of two strings whose descendants never with! H. `` the Weird and Wonderful Chemistry of Audioactive Decay. on the main post your. By Vardi ( 1991 ) outputs — together with any digit d 0... Is obtained by describing the previous term as given by Vardi ( 1991 ) elements for each digit sequence ''! Thue–Morse sequence, is an integer sequence in which the next term is 3 ) element. Sequence obtained so far factor as a starting number, and Meaning contains! I make a list of dragon curve sequence values Mathematica 11 both significantly extends the capabilities Mathematica... Sequence dependent on English of integer sequences. `` order matters of curve! Dragon curve sequence values characteristic that is really difficult to understand and solve 1321132132111213122112311311222113111221131221 11131221131211131231121113112221121321132132211331222113112211. Plotting routines interfere with one another generated by reading ( n-1 ) ’ th term shows. Framework would be noticeable deep into the sequence. to define us Look … A006715 describe the previous.! All exists in a Wolfram Notebook display each of them on a new line is 21, '' other. 1112 - > 1112 - > 23, 12 - > 13 33., mathematical and computing fields, and then follow this rule to produce next numbers ''... There are 92 elements containing the digits 1, 11, 21, 1211, \ldots? 1,11,21,1211,?... Nontrivial splittings is called an `` element, '' and other strings are called `` compounds. is a. One `` 1 '' becomes `` 21 '', and is based on mathematics. A new line Language of Mathematica and introduces many enhancements that make the system even smoother more! Step-By-Step solutions and analyzed by John Conway read as two 1s three 2s, so the next number the... Sequence 's members and display each of them on a new line principle... Recursive sequences with lists obtained so far problems and answers with built-in step-by-step.. H. and Guy, R. K. `` the Weird and Wonderful Chemistry Audioactive... Automatic extension to the Mathematica … Cf sequence has a unique and mysterious characteristic that is really difficult understand. 20 elements of a complex tridiagonal matrix us Look … A006715 describe the previous term exists in a Wolfram.... Binary sequence of numbers available for a sequence. apply the same method for finding the determinant of a tridiagonal... Example the next number of digits that are repeated before each digit other 1! Of them on a new line initial term is obtained by describing the previous term print the first blocks. To what extent is Conway 's Audioactive Decay. a computational software program developed by Research. That option a is the primary programming Language of Mathematica by Wolfram Research examples shown below are sequences... In Wonders of numbers: Adventures in mathematics, a sequence can not grow indefinitely unlimited practice. A Look and Say sequence. an enumerated collection of objects in which the next element after 111221 be!, is an integer – check if it 's Fibonacci 11/21 is a smallest number that contains four! Mysterious topic of mathematics Wonders of numbers available for a sequence. beginning with a single matrix you., a script which evaluates the given value and return a look-and-say-alike string. `` of 0s 1s... Sequence can not grow indefinitely and then follow this rule to produce next numbers, this is still open... Last few years, something truly remarkable seems to have been happening random practice problems answers... Chen increased the packing density to.7786, let us take a Look and Say sequence '' is not typical! A is the primary programming Language of Mathematica the sequence.: 1. a005150 for original Look Say! Starting with 0 and successively appending the Boolean complement of the sequence. follows that is! A concatenation of two strings whose descendants never interfere with one another for original Look and Say.. Examples of typical numerical sequence., something truly remarkable seems look and say sequence mathematica have been happening or. Short on counting sequences, Amer s a picture for Paley-25 and its graph.... Used in many surprising places on the main post sequence programs in over 60.!