A006711 Describe previous term from the right (method A - initial term is 1). (Formerly M4778)

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

Offset

1,2

Comments

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

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A163288 A092806 A138485 * A005151 A098155 A098154

Adjacent sequences: A006708 A006709 A006710 * A006712 A006713 A006714

Keyword

nonn,base,easy,nice

Author

N. J. A. Sloane

Status

approved