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

1,1

Comments

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

Links

Table of n, a(n) for n=1..34.

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

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 *)

Prog

(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; }

Crossrefs

Cf. A000069, A001969, A230454.

Sequence in context: A230176 A033874 A122092 * A372019 A369081 A346909

Adjacent sequences: A230492 A230493 A230494 * A230496 A230497 A230498

Keyword

nonn,base

Author

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

Extensions

a(26) from Michel Marcus, Dec 10 2018

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

Status

approved