cp's OEIS Frontend

A099352 From P-positions in a certain game.

%I A099352 #13 Mar 10 2023 08:07:34
%S A099352 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,
%T A099352 30,31,32,33,34,36,37,38,39,40,41,42,43,44,46,47,48,49,50,51,52,53,54,
%U A099352 55,57,58,59,60,61,62,63,64,65,66,67,69,70,71,72,73,74,75
%N A099352 From P-positions in a certain game.
%H A099352 Nathaniel Johnston, <a href="/A099352/b099352.txt">Table of n, a(n) for n = 0..10000</a>
%H A099352 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 A099352 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.
%p A099352 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 A099352 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:
%p A099352 seq(a(n), n=0..70); # _Nathaniel Johnston_, Apr 28 2011
%t A099352 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 A099352 b[n_] := b[n] = If[n == 0, 0, b[n - 1] + a[n] - Floor[(a[n - 1] + 1)/a[n]] + 2];
%t A099352 Table[a[n], {n, 0, 70}] (* _Jean-François Alcover_, Mar 10 2023, after _Nathaniel Johnston_ *)
%Y A099352 Cf. A099353.
%K A099352 nonn,easy
%O A099352 0,3
%A A099352 _N. J. A. Sloane_, Nov 16 2004