A099355 From P-positions in a certain game.

0, 4, 10, 14, 21, 25, 27, 31, 33, 38, 44, 48, 55, 59, 61, 65, 67, 71, 74, 78, 84, 89, 92, 96, 102, 107, 110, 114, 120, 124, 131, 135, 137, 141, 143, 148, 154, 158, 165, 169, 171, 175, 177, 181, 184, 188, 194, 199, 202, 206, 212, 217, 220, 224, 230, 235, 237

Offset

0,2

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

See A099354.

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) - a(n-1) + a(n) + (-1)^b(n-1) - (-1)^a(n-1) + 3: fi: end:
seq(b(n), n=0..70); # Nathaniel Johnston, Apr 28 2011

Mathematica

a[n_] := a[n] = Module[{j, t}, If[n == 0, 0, t = a[n - 1] + 1; For[j = 0, j <= n - 1, j++, Which[t == b[j], Return[t + 1], t < b[j], Break[]]]; t]];
b[n_] := b[n] = If[n == 0, 0, b[n - 1] - a[n - 1] + a[n] + (-1)^b[n - 1] - (-1)^a[n - 1] + 3];
Table[b[n], {n, 0, 70}] (* Jean-François Alcover, Mar 10 2023, after Nathaniel Johnston *)

Crossrefs

Sequence in context: A114335 A302087 A329103 * A161366 A310424 A176551

Adjacent sequences: A099352 A099353 A099354 * A099356 A099357 A099358

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 16 2004

Status

approved