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A099353 From P-positions in a certain game.

%I A099353 #15 Mar 10 2023 08:07:50
%S A099353 0,2,7,12,18,25,35,45,56,68,83,98,114,131,149,170,191,213,236,260,285,
%T A099353 313,341,370,400,431,463,496,530,565,603,641,680,720,761,803,846,890,
%U A099353 935,983,1031,1080,1130,1181,1233,1286,1340,1395,1451,1510,1569
%N A099353 From P-positions in a certain game.
%H A099353 Nathaniel Johnston, <a href="/A099353/b099353.txt">Table of n, a(n) for n = 0..10000</a>
%H A099353 A. S. Fraenkel, <a href="http://www.emis.de/journals/INTEGERS/papers/eg6/eg6.Abstract.html">New games related to old and new sequences</a>, INTEGERS, Electronic J. of Combinatorial Number Theory, Vol. 4, Paper G6, 2004.
%F A099353 See A099352.
%p A099353 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:
%p A099353 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
%t A099353 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]];
%t A099353 b[n_] := b[n] = If[n == 0,  0, b[n - 1] + a[n] - Floor[(a[n - 1] + 1)/a[n]] + 2];
%t A099353 Table[b[n], {n, 0, 50}] (* _Jean-François Alcover_, Mar 10 2023, after _Nathaniel Johnston_ *)
%K A099353 nonn,easy
%O A099353 0,2
%A A099353 _N. J. A. Sloane_, Nov 16 2004