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

0,2

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 A099352.

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) - floor((a(n-1)+1)/a(n)) + 2: fi: end:seq(b(n), n=0..50); # 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] - Floor[(a[n - 1] + 1)/a[n]] + 2];
Table[b[n], {n, 0, 50}] (* Jean-François Alcover, Mar 10 2023, after Nathaniel Johnston *)

Crossrefs

Sequence in context: A019592 A220120 A131190 * A297432 A299401 A188039

Adjacent sequences: A099350 A099351 A099352 * A099354 A099355 A099356

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 16 2004

Status

approved