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A342641 Numbers k such that A342640(k) = k.

%I A342641 #9 Mar 20 2021 14:37:38
%S A342641 0,2,6,10,14,22,30,38,42,46,54,62,78,94,110,126,142,150,158,170,174,
%T A342641 182,190,206,222,238,254,286,310,318,350,382,414,438,446,478,510,542,
%U A342641 558,574,606,622,638,670,682,686,702,734,750,766,798,830,862,894,926
%N A342641 Numbers k such that A342640(k) = k.
%C A342641 All terms are even.
%C A342641 For any m >= 0:
%C A342641 - let s(m) be the unique finite set of nonnegative integers such that m = Sum_{e in s(m)} 2^e,
%C A342641 - this sequence contains the numbers k such that s(k) is the set of nonnegative integers that are not the sum of two nonnegative integers not in s(k).
%H A342641 Rémy Sigrist, <a href="/A342641/b342641.txt">Table of n, a(n) for n = 1..10000</a>
%e A342641 The first terms, alongside the corresponding sets, are:
%e A342641   n   a(n)  s(a(n))
%e A342641   --  ----  ---------------
%e A342641    1     0  {}
%e A342641    2     2  {1}
%e A342641    3     6  {1, 2}
%e A342641    4    10  {1, 3}
%e A342641    5    14  {1, 2, 3}
%e A342641    6    22  {1, 2, 4}
%e A342641    7    30  {1, 2, 3, 4}
%e A342641    8    38  {1, 2, 5}
%e A342641    9    42  {1, 3, 5}
%e A342641   10    46  {1, 2, 3, 5}
%e A342641   11    54  {1, 2, 4, 5}
%e A342641   12    62  {1, 2, 3, 4, 5}
%e A342641   13    78  {1, 2, 3, 6}
%e A342641   14    94  {1, 2, 3, 4, 6}
%e A342641   15   110  {1, 2, 3, 5, 6}
%o A342641 (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==n) }
%Y A342641 Cf. A133457, A342639, A342640, A342642.
%K A342641 nonn,base
%O A342641 1,2
%A A342641 _Rémy Sigrist_, Mar 17 2021