A099353 From P-positions in a certain game.

0, 2, 7, 12, 18, 25, 35, 45, 56, 68, 83, 98, 114, 131, 149, 170, 191, 213, 236, 260, 285, 313, 341, 370, 400, 431, 463, 496, 530, 565, 603, 641, 680, 720, 761, 803, 846, 890, 935, 983, 1031, 1080, 1130, 1181, 1233, 1286, 1340, 1395, 1451, 1510, 1569

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.

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[b[n], {n, 0, 50}] (* Jean-François Alcover, Mar 10 2023, after Nathaniel Johnston *)

Formula

See A099352.