login
Numbers k such that A342640(k) = 0.
4

%I #8 Mar 20 2021 14:37:45

%S 0,4,8,16,20,24,32,36,40,48,64,68,72,80,84,88,96,100,104,112,128,132,

%T 136,144,148,152,160,164,168,176,192,196,200,208,216,224,228,256,260,

%U 264,272,276,280,288,292,296,304,320,324,328,336,340,344,352,356,360

%N Numbers k such that A342640(k) = 0.

%C For any m >= 0:

%C - let s(m) be the unique finite set of nonnegative integers such that m = Sum_{e in s(m)} 2^e,

%C - this sequence contains the numbers k such that every nonnegative integer is the sum of two nonnegative integers not in s(k).

%C All terms are even.

%H Rémy Sigrist, <a href="/A342642/b342642.txt">Table of n, a(n) for n = 1..10000</a>

%e The first terms, alongside the corresponding sets, are:

%e n a(n) s(a(n))

%e -- ---- ---------

%e 1 0 {}

%e 2 4 {2}

%e 3 8 {3}

%e 4 16 {4}

%e 5 20 {2, 4}

%e 6 24 {3, 4}

%e 7 32 {5}

%e 8 36 {2, 5}

%e 9 40 {3, 5}

%e 10 48 {4, 5}

%e 11 64 {6}

%e 12 68 {2, 6}

%e 13 72 {3, 6}

%e 14 80 {4, 6}

%e 15 84 {2, 4, 6}

%o (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 Cf. A133457, A342639, A342640, A342641.

%K nonn,base

%O 1,2

%A _Rémy Sigrist_, Mar 17 2021