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A342642 Numbers k such that A342640(k) = 0.

%I A342642 #8 Mar 20 2021 14:37:45
%S A342642 0,4,8,16,20,24,32,36,40,48,64,68,72,80,84,88,96,100,104,112,128,132,
%T A342642 136,144,148,152,160,164,168,176,192,196,200,208,216,224,228,256,260,
%U A342642 264,272,276,280,288,292,296,304,320,324,328,336,340,344,352,356,360
%N A342642 Numbers k such that A342640(k) = 0.
%C A342642 For any m >= 0:
%C A342642 - let s(m) be the unique finite set of nonnegative integers such that m = Sum_{e in s(m)} 2^e,
%C A342642 - this sequence contains the numbers k such that every nonnegative integer is the sum of two nonnegative integers not in s(k).
%C A342642 All terms are even.
%H A342642 Rémy Sigrist, <a href="/A342642/b342642.txt">Table of n, a(n) for n = 1..10000</a>
%e A342642 The first terms, alongside the corresponding sets, are:
%e A342642   n   a(n)  s(a(n))
%e A342642   --  ----  ---------
%e A342642    1     0  {}
%e A342642    2     4  {2}
%e A342642    3     8  {3}
%e A342642    4    16  {4}
%e A342642    5    20  {2, 4}
%e A342642    6    24  {3, 4}
%e A342642    7    32  {5}
%e A342642    8    36  {2, 5}
%e A342642    9    40  {3, 5}
%e A342642   10    48  {4, 5}
%e A342642   11    64  {6}
%e A342642   12    68  {2, 6}
%e A342642   13    72  {3, 6}
%e A342642   14    80  {4, 6}
%e A342642   15    84  {2, 4, 6}
%o A342642 (PARI) is(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==0) }
%Y A342642 Cf. A133457, A342639, A342640, A342641.
%K A342642 nonn,base
%O A342642 1,2
%A A342642 _Rémy Sigrist_, Mar 17 2021