A180938 -id:A180938 - cp's OEIS frontend

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

Rémy Sigrist, Feb 27 2023

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

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

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

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

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

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

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

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

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

A351836 Smallest evil number k (member of A001969) such that k*n is also evil.

Original entry on oeis.org

3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 5, 9, 15, 3, 33, 3, 3, 3, 3, 3, 3, 3, 5, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 3, 3, 3, 5, 3, 9, 9, 15, 3, 3, 3, 33, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 3, 3, 5, 3, 3, 3, 3, 3, 3, 3, 3

Offset: 1

Jeffrey Shallit, Feb 21 2022

All terms are odd since if 2*j and 2*j*n are both evil, then so are j and j*n. - Michael S. Branicky, Feb 21 2022

			For n = 7 both 9 and 9*7 are evil and no smaller multiple of 7 works.

Cf. A001969, A351835 (analog for the odious numbers A000069).

Cf. A180938 (where k is not necessarily evil).

evilQ[n_] := EvenQ[DigitCount[n, 2, 1]]; a[n_] := Module[{k = 1}, While[!evilQ[k] || !evilQ[k*n], k++]; k]; Array[a, 100] (* Amiram Eldar, Feb 21 2022 *)

isevil(m) = !(hammingweight(m) % 2);
a(n) = my(k=1); while (!isevil(k) || !isevil(k*n), k++); k; \\ Michel Marcus, Feb 22 2022

def ev(n): return bin(n).count("1")%2 == 0
def a(n):
    k = 3
    while not (ev(k) and ev(k*n)): k += 1
    return k
print([a(n) for n in range(1, 87)]) # Michael S. Branicky, Feb 21 2022

cp's OEIS Frontend

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

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