A360981 a(n) is the least positive multiple of n that is an evil number (A001969).

3, 6, 3, 12, 5, 6, 63, 24, 9, 10, 33, 12, 39, 126, 15, 48, 17, 18, 57, 20, 63, 66, 23, 24, 75, 78, 27, 252, 29, 30, 1023, 96, 33, 34, 105, 36, 111, 114, 39, 40, 123, 126, 43, 132, 45, 46, 141, 48, 147, 150, 51, 156, 53, 54, 165, 504, 57, 58, 177, 60, 183, 2046

Offset: 1

Author

Rémy Sigrist, Feb 27 2023

Keywords

• nonn
• base
• look

Comments

This sequence is well defined: for any n > 0, A020330(n) is both a multiple of n and an evil number.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001969, A020330, A180938, A360980 (variant for odious numbers).

Programs

Maple

f:= proc(n) local k;
  for k from n by n do
    if convert(convert(k,base,2),`+`)::even then return k fi
  od
end proc:
map(f, [$1..100]); # Robert Israel, Mar 29 2023

Mathematica

a[n_] := Module[{k = n}, While[OddQ[DigitCount[k, 2, 1]], k +=n]; k]; Array[a, 100] (* Amiram Eldar, Aug 07 2023 *)

PARI

a(n) = { forstep (m=n, oo, n, if (hammingweight(m)%2==0, return (m))) }

Python

def A360981(n):
    k = n
    while k.bit_count()&1:
        k += n
    return k # Chai Wah Wu, Feb 28 2023

Formula

a(n) = A180938(n) * n.

a(n) = n iff n belongs to A001969.