A099352 From P-positions in a certain game.

0, 1, 3, 4, 5, 6, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 73, 74, 75

Offset: 0

Author

N. J. A. Sloane, Nov 16 2004

Keywords

• nonn
• easy

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.

Crossrefs

Cf. A099353.

Programs

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(tNathaniel 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] - Floor[(a[n - 1] + 1)/a[n]] + 2];
Table[a[n], {n, 0, 70}] (* Jean-François Alcover, Mar 10 2023, after Nathaniel Johnston *)

Formula

Let a(n) = this sequence, b(n) = A099353. 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) + a(n) - floor((a(n-1)+1)/a(n)) + 2. Apart from initial zero, this is the complement of A099353.