A356150 a(n) is the sum of the positive integers whose binary expansion appears as a substring in the binary expansion of n or its complement.

1, 3, 4, 10, 8, 12, 11, 25, 25, 18, 26, 28, 30, 33, 26, 56, 62, 61, 56, 56, 39, 63, 64, 67, 62, 66, 72, 77, 80, 78, 57, 119, 139, 143, 137, 135, 134, 119, 134, 134, 134, 81, 120, 138, 139, 147, 142, 146, 147, 148, 132, 153, 140, 157, 165, 165, 168, 174, 181

Offset

1,2

Comments

Leading 0's in binary expansions are ignored.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..8192

Index entries for sequences related to binary expansion of n

Formula

a(n) >= A078823(n).

a(n) Sum_{k = 1..A356148(n)} A356149(n, k).

Example

For n = 11:
- row 11 of A356149 is 1, 2, 3, 4, 5, 11,
- so a(11) = 1 + 2 + 3 + 4 + 5 + 11 = 26.

Prog

(PARI) a(n) = { my (b=binary(n)); vecsum(setbinop((i, j) -> my (s=fromdigits(b[i..j], 2)); if (b[i], s, 2^(j-i+1)-1-s), [1..#b])) }
(Python)
def a(n):
    N = n.bit_length()
    c, s = ((1<<N)-1)^n, set()
    for i in range(N):
        for l in range(N-i):
            mask = ((2<<l)-1) << i
            s.add((mask&n) >> i)
            s.add((mask&c) >> i)
    return sum(s)
print([a(n) for n in range(1, 60)]) # Michael S. Branicky, Jul 28 2022

Crossrefs

Cf. A078823, A356148, A356149.

Sequence in context: A328711 A361655 A343876 * A222136 A339652 A279787

Adjacent sequences: A356147 A356148 A356149 * A356151 A356152 A356153

Keyword

nonn,base

Author

Rémy Sigrist, Jul 28 2022

Status

approved