A350802 a(n) is the sum of the numbers k < n such that a(k) AND n = a(k) (where AND denotes the bitwise AND operator).

0, 0, 1, 3, 1, 7, 1, 21, 1, 21, 1, 34, 1, 43, 1, 65, 1, 73, 1, 94, 1, 127, 1, 157, 1, 157, 1, 186, 1, 227, 1, 265, 1, 273, 12, 287, 1, 309, 12, 328, 1, 349, 12, 376, 115, 463, 126, 495, 1, 397, 12, 411, 1, 465, 12, 484, 1, 505, 12, 532, 277, 797, 288, 829, 1

Offset

0,4

Comments

The definition is recursive: a(n) depends on prior terms (a(0), ..., a(n-1)); a(0) = a(1) = 0 correspond to empty sums.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Example

The first terms, alongside the corresponding k's, are:
  n   a(n)  k's
  --  ----  -------------------------
   0     0  {}
   1     0  {0}
   2     1  {0, 1}
   3     3  {0, 1, 2}
   4     1  {0, 1}
   5     7  {0, 1, 2, 4}
   6     1  {0, 1}
   7    21  {0, 1, 2, 3, 4, 5, 6}
   8     1  {0, 1}
   9    21  {0, 1, 2, 4, 6, 8}
  10     1  {0, 1}
  11    34  {0, 1, 2, 3, 4, 6, 8, 10}
  12     1  {0, 1}

Maple

a:= proc(n) option remember; add(
     `if`(Bits[And](n, a(j))=a(j), j, 0), j=0..n-1)
    end:
seq(a(n), n=0..80);  # Alois P. Heinz, Feb 28 2022

Prog

(PARI) for (n=1, #a=vector(65), print1 (a[n]=sum(k=1, n-1, if (bitand(a[k], n-1)==a[k], k-1, 0))", "))

Crossrefs

Cf. A350677, A351887.

Sequence in context: A290422 A352402 A278954 * A331884 A146430 A146281

Adjacent sequences: A350799 A350800 A350801 * A350803 A350804 A350805

Keyword

base,nonn

Author

Rémy Sigrist, Feb 25 2022

Status

approved