A342640 a(n) = A342639(n, n).

0, 3, 2, 15, 0, 11, 6, 63, 0, 3, 10, 47, 8, 27, 14, 255, 0, 3, 2, 15, 0, 43, 22, 191, 0, 35, 10, 111, 24, 59, 30, 1023, 0, 3, 2, 15, 0, 11, 38, 63, 0, 3, 42, 175, 8, 91, 46, 767, 0, 3, 2, 143, 32, 43, 54, 447, 32, 99, 42, 239, 56, 123, 62, 4095, 0, 3, 2, 15, 0

Offset

0,2

Comments

For any n >= 0:

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

- then s(a(n)) corresponds to the set of nonnegative integers that are not the sum of two nonnegative integers not in s(n).

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8192

Formula

a(2^n-1) = 4^n-1.

Example

The first terms, alongside the corresponding sets, are:
  n   a(n)  s(n)          s(a(n))
  --  ----  ------------  ------------------------
   0     0  {}            {}
   1     3  {0}           {0, 1}
   2     2  {1}           {1}
   3    15  {0, 1}        {0, 1, 2, 3}
   4     0  {2}           {}
   5    11  {0, 2}        {0, 1, 3}
   6     6  {1, 2}        {1, 2}
   7    63  {0, 1, 2}     {0, 1, 2, 3, 4, 5}
   8     0  {3}           {}
   9     3  {0, 3}        {0, 1}
  10    10  {1, 3}        {1, 3}
  11    47  {0, 1, 3}     {0, 1, 2, 3, 5}
  12     8  {2, 3}        {3}
  13    27  {0, 2, 3}     {0, 1, 3, 4}
  14    14  {1, 2, 3}     {1, 2, 3}
  15   255  {0, 1, 2, 3}  {0, 1, 2, 3, 4, 5, 6, 7}

Prog

(PARI) a(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) }

Crossrefs

Cf. A133457, A342639, A342641, A342642.

Sequence in context: A145747 A055234 A291051 * A204990 A367741 A328282

Adjacent sequences: A342637 A342638 A342639 * A342641 A342642 A342643

Keyword

nonn,base

Author

Rémy Sigrist, Mar 17 2021

Status

approved