A351886 -id:A351886 - cp's OEIS frontend

A350677 a(n) is the sum of the numbers k < n such that a(k) AND n = 0 (where AND denotes the bitwise AND operator).

0, 0, 1, 1, 6, 1, 11, 1, 22, 13, 18, 1, 39, 11, 29, 1, 88, 5, 70, 1, 82, 1, 84, 1, 158, 23, 124, 1, 134, 1, 163, 1, 428, 151, 272, 73, 328, 117, 315, 87, 452, 185, 307, 97, 258, 109, 228, 35, 444, 171, 331, 77, 378, 81, 265, 37, 345, 135, 251, 41, 238, 45, 194

Offset: 0

Rémy Sigrist, Feb 25 2022

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

			The first terms, alongside the corresponding k's, are:
  n   a(n)  k's
  --  ----  --------------------------
   0     0  {}
   1     0  {0}
   2     1  {0, 1}
   3     1  {0, 1}
   4     6  {0, 1, 2, 3}
   5     1  {0, 1}
   6    11  {0, 1, 2, 3, 5}
   7     1  {0, 1}
   8    22  {0, 1, 2, 3, 4, 5, 7}
   9    13  {0, 1, 4, 8}
  10    18  {0, 1, 2, 3, 5, 7}
  11     1  {0, 1}
  12    39  {0, 1, 2, 3, 5, 7, 10, 11}

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

Cf. A350802, A351886.

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

for (n=1, #a=vector(63), print1 (a[n]=sum(k=1, n-1, if (bitand(a[k], n-1)==0, k-1, 0))", "))

A351887 a(n) is the number of k < n such that a(k) AND n = a(k) (where AND denotes the bitwise AND operator).

Original entry on oeis.org

0, 1, 1, 3, 1, 4, 2, 7, 1, 5, 2, 8, 3, 8, 6, 15, 1, 6, 3, 11, 2, 8, 7, 18, 4, 9, 8, 19, 7, 14, 14, 31, 1, 7, 4, 13, 4, 12, 10, 24, 5, 12, 9, 21, 11, 22, 19, 40, 1, 8, 5, 17, 5, 18, 13, 35, 8, 19, 15, 34, 15, 32, 28, 63, 1, 9, 4, 15, 6, 18, 12, 31, 7, 18, 11

Offset: 0

Rémy Sigrist, Feb 23 2022

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

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

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

Cf. A088167, A350802, A351886.

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

for (n=1, #a=vector(75), print1 (a[n]=sum(k=1, n-1, bitand(a[k], n-1)==a[k])", "))

a = []
[a.append(sum(a[k] & n == a[k] for k in range(n))) for n in range(75)]
print(a) # Michael S. Branicky, Feb 24 2022

cp's OEIS Frontend

A350677 a(n) is the sum of the numbers k < n such that a(k) AND n = 0 (where AND denotes the bitwise AND operator).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

PARI