A028352 A Golomb-like recurrence that decreases infinitely often.

2, 8, 6, 4, 2, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 72, 70, 68, 66, 64, 62, 60, 58, 56, 54, 52, 50, 48, 46, 44, 42, 40, 38, 36, 34, 32, 30, 28, 26, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 216, 214, 212, 210, 208, 206, 204, 202

Offset

1,1

Comments

The sequence is a solution to the recursion a(a(n) + n) = a(n) + 4n, which is similar to the Golomb recursion b(b(n) + kn) = 2b(n) + kn, k=1,2,...

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

E. J. Barbeau, J. Chew and S. Tanny, A matrix dynamics approach to Golomb's recursion, Electronic J. Combinatorics, #4.1 16 1997.

Formula

a(1)=1, a(2*3^m+r) = 8*3^m - 2r with m=0, 1, 2, ..., 0 <= r <= 4*3^m - 1. - Ralf Stephan, Jan 16 2003

a(n) = 12*3^floor(log(n/2)/log(3)) - 2*n. - Benoit Cloitre, Jan 23 2003

Mathematica

Table[12*3^Floor[Log[n/2]/Log[3]] - 2*n , {n, 1, 50}] (* G. C. Greubel, Nov 27 2016 *)

Prog

(PARI) a(n) = if(n==1, 2, m=floor(log(n/2)/log(3)); r=n-2*3^m; 8*3^m-2*r)

Crossrefs

Sequence in context: A175803 A019986 A146943 * A132699 A347634 A248413

Adjacent sequences: A028349 A028350 A028351 * A028353 A028354 A028355

Keyword

nonn,easy

Author

Simon Plouffe

Extensions

Edited by Ralf Stephan, Jan 16 2003

Status

approved