A390089 Positive numbers that are divisible by their binary ones' complement.

2, 6, 10, 12, 14, 30, 42, 54, 56, 60, 62, 126, 170, 204, 238, 240, 250, 252, 254, 438, 504, 510, 682, 930, 990, 992, 1012, 1020, 1022, 1958, 2024, 2046, 2730, 3276, 3510, 3640, 3780, 3822, 3900, 3978, 3990, 4004, 4030, 4032, 4050, 4056, 4060, 4074, 4080, 4082

Offset

1,1

Comments

As the ones' complement of an odd number is even, no terms are odd.

All terms of A020988 and A000918 are terms of this sequence.

Links

Scott R. Shannon, Table of n, a(n) for n = 1..1551

Formula

10 is a term as 10 = 1010_2 that has a ones' complement of 101_2 = 5, and 10 is divisible by 5.

Mathematica

q[n_] := Module[{k = 2^IntegerLength[n, 2] - n - 1}, k > 0 && Divisible[n, k]]; Select[Range[2, 4100, 2], q] (* Amiram Eldar, Jan 17 2026 *)

Prog

(Python)
def ok(n): return (c := (n^((1 << n.bit_length()) - 1))) and n%c == 0
print([k for k in range(4083) if ok(k)]) # Michael S. Branicky, Jan 17 2026

Crossrefs

Cf. A035327, A349932, A035928, A020988, A000918.

Sequence in context: A264964 A374918 A195064 * A328926 A055743 A354424

Adjacent sequences: A390086 A390087 A390088 * A390090 A390091 A390092

Keyword

nonn,base

Author

Scott R. Shannon, Jan 15 2026

Status

approved