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

0, 2, 6, 10, 14, 22, 30, 38, 42, 46, 54, 62, 78, 94, 110, 126, 142, 150, 158, 170, 174, 182, 190, 206, 222, 238, 254, 286, 310, 318, 350, 382, 414, 438, 446, 478, 510, 542, 558, 574, 606, 622, 638, 670, 682, 686, 702, 734, 750, 766, 798, 830, 862, 894, 926

Offset

1,2

Comments

All terms are even.

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 s(k) is the set of nonnegative integers that are not the sum of two nonnegative integers not in s(k).

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     2  {1}
   3     6  {1, 2}
   4    10  {1, 3}
   5    14  {1, 2, 3}
   6    22  {1, 2, 4}
   7    30  {1, 2, 3, 4}
   8    38  {1, 2, 5}
   9    42  {1, 3, 5}
  10    46  {1, 2, 3, 5}
  11    54  {1, 2, 4, 5}
  12    62  {1, 2, 3, 4, 5}
  13    78  {1, 2, 3, 6}
  14    94  {1, 2, 3, 4, 6}
  15   110  {1, 2, 3, 5, 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==n) }

Crossrefs

Cf. A133457, A342639, A342640, A342642.

Sequence in context: A192109 A216090 A378458 * A118369 A226829 A236423

Adjacent sequences: A342638 A342639 A342640 * A342642 A342643 A342644

Keyword

nonn,base

Author

Rémy Sigrist, Mar 17 2021

Status

approved