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

0, 4, 8, 16, 20, 24, 32, 36, 40, 48, 64, 68, 72, 80, 84, 88, 96, 100, 104, 112, 128, 132, 136, 144, 148, 152, 160, 164, 168, 176, 192, 196, 200, 208, 216, 224, 228, 256, 260, 264, 272, 276, 280, 288, 292, 296, 304, 320, 324, 328, 336, 340, 344, 352, 356, 360

Offset

1,2

Comments

For any m >= 0:

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

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

All terms are even.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Example

The first terms, alongside the corresponding sets, are:
  n   a(n)  s(a(n))
  --  ----  ---------
   1     0  {}
   2     4  {2}
   3     8  {3}
   4    16  {4}
   5    20  {2, 4}
   6    24  {3, 4}
   7    32  {5}
   8    36  {2, 5}
   9    40  {3, 5}
  10    48  {4, 5}
  11    64  {6}
  12    68  {2, 6}
  13    72  {3, 6}
  14    80  {4, 6}
  15    84  {2, 4, 6}

Prog

(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) }

Crossrefs

Cf. A133457, A342639, A342640, A342641.

Sequence in context: A312792 A312793 A104235 * A036993 A143718 A031399

Adjacent sequences: A342639 A342640 A342641 * A342643 A342644 A342645

Keyword

nonn,base

Author

Rémy Sigrist, Mar 17 2021

Status

approved