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

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

1,1

Comments

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

Links

Table of n, a(n) for n=1..86.

Example

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

Mathematica

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 *)

Prog

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

Crossrefs

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

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

Sequence in context: A210746 A283986 A343515 * A105159 A365458 A334625

Adjacent sequences: A351833 A351834 A351835 * A351837 A351838 A351839

Keyword

nonn,base

Author

Jeffrey Shallit, Feb 21 2022

Status

approved