A099356 - OEIS

A099356

From P-positions in a certain game.

0, 1, 3, 4, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 0..10000

A. S. Fraenkel, New games related to old and new sequences, INTEGERS, Electronic J. of Combinatorial Number Theory, Vol. 4, Paper G6, 2004.

FORMULA

Let a(n) = this sequence, b(n) = A099357. Then a(n) = the smallest number not in {a(0), b(0), a(1), b(1), ..., a(n-1), b(n-1)}; b(n) = b(n-1) + (-1)^a(n-1)*a(n-1) + a(n) + 1. Apart from initial zero, complement of A099357.

MAPLE

a:=proc(n) option remember: local j, t: if(n=0)then return 0: else t:=a(n-1)+1: for j from 0 to n-1 do if(t=b(j))then return t+1: elif(t<b(j))then break: fi: od: return t: fi: end:

b:=proc(n) option remember: if(n=0)then return 0: else return b(n-1) + (-1)^a(n-1)*a(n-1) + a(n) + 1: fi: end:

seq(a(n), n=0..70); # Nathaniel Johnston, Apr 28 2011

CROSSREFS

Cf. A099352 - A099355.

Sequence in context: A072152 A199015 A196098 * A377431 A325209 A121543

Adjacent sequences: A099353 A099354 A099355 * A099357 A099358 A099359

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Nov 16 2004

STATUS

approved