A006711 Describe previous term from the right (method A - initial term is 1).

1, 11, 21, 1112, 1231, 11131211, 2112111331, 112331122112, 12212221231221, 11221113121132112211, 212221121321121113312221, 113211233112211213111221321112

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy
• nice

Comments

Method A = 'frequency' followed by 'digit'-indication.

Examples

			E.g. the term after 1231 is obtained by saying "one 1, one 3, one 2, one 1", which gives 11131211.
		

References

• J. H. Conway, personal communication.
• Akhlesh Lakhtakia and C. A. Pickover, Observations on the Gleichniszahlen-Reihe: An Unusual Number Theory Sequence, J. Rec. Math., Vol. 25 #3, pp. 189-192, 1993.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..24
• Onno M. Cain, Sela T. Enin, Inventory Loops (i.e. Counting Sequences) have Pre-period 2 max S_1 + 60, arXiv:2004.00209 [math.NT], 2020.
• Trevor Scheopner, The Cyclic Nature (and Other Intriguing Properties) of Descriptive Numbers, Princeton Undergraduate Mathematics Journal, Issue 1, Article 4.
• Eric Weisstein's World of Mathematics, Look and Say Sequence
• Wikipedia, Look-and-say sequence

Crossrefs

Cf. A005150, A022506, A022482, A022507-A022513.

Programs

Haskell

a006711 n = a006711_list !! (n-1)
a006711_list = iterate (a045918 . a004086) 1
-- Reinhard Zumkeller, Mar 02 2014

Mathematica

A006711[1]:=1;A006711[n_]:=A006711[n]=FromDigits[Flatten[{Length[#],First[#]}&/@Split[Reverse[IntegerDigits[A006711[n-1]]]]]];Map[A006711,Range[15]] (* Peter J. C. Moses, Apr 22 2013 *)

Formula

a(n+1) = A045918(A004086(a(n))). - Reinhard Zumkeller, Mar 02 2014