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

Author

Rémy Sigrist, Jul 28 2022

Keywords

• nonn
• base

Comments

Leading 0's in binary expansions are ignored.

Examples

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

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..8192
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A078823, A356148, A356149.

Programs

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<> i)
            s.add((mask&c) >> i)
    return sum(s)
print([a(n) for n in range(1, 60)]) # Michael S. Branicky, Jul 28 2022

Formula

a(n) >= A078823(n).

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