A394533 Binary expansion of a(n) obtained from binary expansion of n with increased number of zeros separated by every next 1 by total number of zeros lying from the left side of selected 1.

1, 2, 3, 4, 10, 6, 7, 8, 36, 20, 42, 12, 26, 14, 15, 16, 136, 72, 292, 40, 164, 84, 170, 24, 100, 52, 106, 28, 58, 30, 31, 32, 528, 272, 2184, 144, 1160, 584, 2340, 80, 648, 328, 1316, 168, 676, 340, 682, 48, 392, 200, 804, 104, 420, 212, 426, 56, 228, 116, 234

Offset

1,2

Comments

Permutation of A225620.

Links

Table of n, a(n) for n=1..59.

Example

Binary expansion of n = 41 is 1(0)1(00)1(), then binary expansion of a(n) is 1(0)1(00,0)1(00,0).

Prog

(PARI) a(n) = my(A = 2*n+1, B = 0, C = 0); forstep(k=logint(n, 2), 0, -1, if(bittest(A, k), B = (1+B<<1)<<C, C++)); B
(Python)
def a(n: int) -> int:
    C, B, A = 0, 0, 2*n + 1
    for k in range(n.bit_length() - 1, -1, -1):
        if (A >> k) & 1: B = (1 + (B << 1)) << C
        else: C += 1
    return B
print([a(n) for n in range(1, 60)])  # Peter Luschny, Mar 28 2026

Crossrefs

Cf. A125106, A225620.

Sequence in context: A356332 A065634 A364223 * A087548 A353959 A242488

Adjacent sequences: A394530 A394531 A394532 * A394534 A394535 A394536

Keyword

nonn,base,easy

Author

Mikhail Kurkov, Mar 24 2026

Status

approved