

A351836


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


1



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
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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 A334625 A209291
Adjacent sequences: A351833 A351834 A351835 * A351837 A351838 A351839


KEYWORD

nonn,base


AUTHOR

Jeffrey Shallit, Feb 21 2022


STATUS

approved



