cp's OEIS Frontend

A342640 a(n) = A342639(n, n).

%I A342640 #9 Mar 20 2021 14:37:30
%S A342640 0,3,2,15,0,11,6,63,0,3,10,47,8,27,14,255,0,3,2,15,0,43,22,191,0,35,
%T A342640 10,111,24,59,30,1023,0,3,2,15,0,11,38,63,0,3,42,175,8,91,46,767,0,3,
%U A342640 2,143,32,43,54,447,32,99,42,239,56,123,62,4095,0,3,2,15,0
%N A342640 a(n) = A342639(n, n).
%C A342640 For any n >= 0:
%C A342640 - let s(n) be the unique finite set of nonnegative integers such that n = Sum_{e in s(n)} 2^e,
%C A342640 - then s(a(n)) corresponds to the set of nonnegative integers that are not the sum of two nonnegative integers not in s(n).
%H A342640 Rémy Sigrist, <a href="/A342640/b342640.txt">Table of n, a(n) for n = 0..8192</a>
%F A342640 a(2^n-1) = 4^n-1.
%e A342640 The first terms, alongside the corresponding sets, are:
%e A342640   n   a(n)  s(n)          s(a(n))
%e A342640   --  ----  ------------  ------------------------
%e A342640    0     0  {}            {}
%e A342640    1     3  {0}           {0, 1}
%e A342640    2     2  {1}           {1}
%e A342640    3    15  {0, 1}        {0, 1, 2, 3}
%e A342640    4     0  {2}           {}
%e A342640    5    11  {0, 2}        {0, 1, 3}
%e A342640    6     6  {1, 2}        {1, 2}
%e A342640    7    63  {0, 1, 2}     {0, 1, 2, 3, 4, 5}
%e A342640    8     0  {3}           {}
%e A342640    9     3  {0, 3}        {0, 1}
%e A342640   10    10  {1, 3}        {1, 3}
%e A342640   11    47  {0, 1, 3}     {0, 1, 2, 3, 5}
%e A342640   12     8  {2, 3}        {3}
%e A342640   13    27  {0, 2, 3}     {0, 1, 3, 4}
%e A342640   14    14  {1, 2, 3}     {1, 2, 3}
%e A342640   15   255  {0, 1, 2, 3}  {0, 1, 2, 3, 4, 5, 6, 7}
%o A342640 (PARI) a(n) = { my (v=0); for (x=0, 2*#binary(n), my (f=0); for (y=0, x, if (!bittest(n,y) && !bittest(n,x-y), f=1; break)); if (!f, v+=2^x)); return (v) }
%Y A342640 Cf. A133457, A342639, A342641, A342642.
%K A342640 nonn,base
%O A342640 0,2
%A A342640 _Rémy Sigrist_, Mar 17 2021