A126616 a(n) = n for n < 10, a(10*n) = a(n), and if the terms a(10), a(20), a(30), ... are deleted, one gets back the original sequence.

1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 5, 1, 3, 4, 2, 5, 1, 3, 4, 2, 6, 5, 1, 3, 4, 2, 6, 5, 1, 3, 7, 4, 2, 6, 5, 1, 3, 7, 4, 2, 8, 6, 5, 1, 3, 7, 4, 2, 8, 6, 9, 5, 1, 3, 7, 4, 2, 8, 6, 9, 1, 5, 1, 3, 7, 4

Offset

1,2

Comments

A self-generating sequence.

Invented by Eric Angelini. Might also be called a lizard sequence (une suite du lézard) because it grows back from its tail.

References

J.-P. Delahaye, La suite du lézard et autres inventions, Pour la Science, No. 353, 2007.

Links

Table of n, a(n) for n=1..105.

Maple

A126616 := proc(n) option remember ; if n < 10 then n ; elif n mod 10 = 0 then A126616(n/10) ; else A126616( n-floor(n/10) ) ; fi ; end: seq(A126616(n), n=1..120) ; # R. J. Mathar, Oct 02 2007

Mathematica

a[n_] := Module[{m = 10, k = n, q}, While[k >= m, q = Quotient[k, m]; If[Mod[k, m] != 0, k -= q, k = q]]; k];
Table[a[n], {n, 1, 105}] (* Jean-François Alcover, Aug 02 2022, after M. F. Hasler *)

Prog

(PARI) a(n, m=10)=while(n>=m, if(n%m, n-=n\m, n\=m)); n \\ M. F. Hasler, Mar 07 2015

Crossrefs

Cf. A117943, A178931, A255824 - A255829.

Sequence in context: A133500 A256229 A052423 * A121042 A369529 A000030

Adjacent sequences: A126613 A126614 A126615 * A126617 A126618 A126619

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 09 2007

Extensions

More terms from R. J. Mathar, Oct 02 2007

Definition rephrased by M. F. Hasler, Mar 09 2015

Status

approved