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

Author

N. J. A. Sloane, Feb 09 2007

Keywords

• nonn
• easy

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.

Crossrefs

Cf. A117943, A178931, A255824 - A255829.

Programs

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 *)

PARI

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

Extensions

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

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