A230495 a(n) is the minimal odd evil k, such that k^i, i=1,2,...,n, all are evil, and a(n)=0, if there is no such k.

3, 3, 3, 27, 287, 287, 287, 287, 783, 783, 783, 19099, 20249, 34391, 80577, 92589, 211183, 211183, 211183, 1995137, 4270443, 4270443, 4270443, 4270443, 17026791, 317108969, 317108969, 317108969, 979104339, 979104339, 6044000725, 21911775681, 21911775681, 26576734759

Offset: 1

Author

Vladimir Shevelev and Peter J. C. Moses, Oct 21 2013

Keywords

• nonn
• base

Comments

We conjecture that a(n)>0 for all n.

Links

• Vladimir Shevelev, "Odious-evil stability" of integers, post to the SeqFan Mailing List, Oct 20 2013.

Crossrefs

Cf. A000069, A001969, A230454.

Programs

Mathematica

fQ[n_] := EvenQ[DigitCount[n, 2,1]]; a[n_] := Module[{k=3}, While[ LengthWhile[ Range[n], fQ[k^#] &] != n, k+=2]; k]; Array[a, 12] (* Amiram Eldar, Dec 10 2018 *)

PARI

isevil(n) = (hammingweight(n) % 2) == 0; \\ A000069
isok(k, n) = {if (!isevil(k), return (0)); for (i=1, n, if (!isevil(k^i), return (0));); return (1);}
a(n) = {my(k=1); while(!isok(k,n), k += 2); k;}

Extensions

a(26) from Michel Marcus, Dec 10 2018

a(27)-a(34) from Amiram Eldar, Aug 03 2023