A361944 a(n) is the least k > 0 such that the binary expansion of k*n is an abelian square (A272653).

3, 5, 1, 9, 2, 6, 9, 17, 1, 1, 3, 3, 10, 11, 1, 33, 2, 2, 10, 26, 3, 6, 2, 22, 6, 5, 2, 21, 25, 5, 33, 65, 1, 1, 18, 1, 6, 5, 4, 13, 15, 14, 1, 3, 1, 1, 5, 11, 3, 3, 1, 3, 1, 1, 3, 41, 9, 37, 11, 10, 3, 39, 1, 129, 2, 2, 3, 2, 9, 9, 8, 11, 3, 3, 2, 27, 2, 2, 3

Offset

1,1

Links

Table of n, a(n) for n=1..79.

Index entries for sequences related to binary expansion of n

Formula

a(n) = A361943(n) / n.

a(n) = 1 iff n belongs to A272653.

Example

a(8) = A361943(8)/8 = 136/8 = 17.

Prog

(PARI) a(n) = { forstep (m = n, oo, n, my (w = #binary(m)); if (w%2==0 && hammingweight(m)==2*hammingweight(m % (2^(w/2))), return (m/n))) }
(Python)
from itertools import count
def a(n): return next(m//n for m in count(n, n) if not (w:= m.bit_length())&1 and m.bit_count() == ((m>>(w>>1)).bit_count())<<1)
print([a(n) for n in range(1, 80)]) # Michael S. Branicky, Mar 31 2023 after Rémy Sigrist

Crossrefs

Cf. A272653, A361943.

Sequence in context: A235605 A212695 A209422 * A320386 A112411 A283838

Adjacent sequences: A361941 A361942 A361943 * A361945 A361946 A361947

Keyword

nonn,base

Author

Rémy Sigrist, Mar 31 2023

Status

approved