A361943 a(n) is the least multiple of n whose binary expansion is an abelian square (A272653).

3, 10, 3, 36, 10, 36, 63, 136, 9, 10, 33, 36, 130, 154, 15, 528, 34, 36, 190, 520, 63, 132, 46, 528, 150, 130, 54, 588, 725, 150, 1023, 2080, 33, 34, 630, 36, 222, 190, 156, 520, 615, 588, 43, 132, 45, 46, 235, 528, 147, 150, 51, 156, 53, 54, 165, 2296, 513

Offset

1,1

Comments

This sequence is well defined as for any n > 0, A020330(n) is a multiple of n and its binary expansion is an abelian square.

Links

Table of n, a(n) for n=1..57.

Index entries for sequences related to binary expansion of n

Formula

a(n) = A361944(n) * n.

a(n) <= A020330(n).

a(n) >= n with equality iff n belongs to A272653.

Example

The first terms, alongside their binary expansion, are:
  n   a(n)  bin(a(n))
  --  ----  ----------
   1     3          11
   2    10        1010
   3     3          11
   4    36      100100
   5    10        1010
   6    36      100100
   7    63      111111
   8   136    10001000
   9     9        1001
  10    10        1010
  11    33      100001
  12    36      100100
  13   130    10000010
  14   154    10011010
  15    15        1111
  16   528  1000010000

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))) }
(Python)
from itertools import count
def a(n): return next(m 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, 60)]) # Michael S. Branicky, Mar 31 2023 after Rémy Sigrist

Crossrefs

Cf. A020330, A272653, A361944.

Sequence in context: A072988 A170855 A338683 * A320583 A339317 A131814

Adjacent sequences: A361940 A361941 A361942 * A361944 A361945 A361946

Keyword

nonn,base

Author

Rémy Sigrist, Mar 31 2023

Status

approved