A230496 a(n) is the minimal odd odious k > 1, such that k^i, i=1,2,...,n, all are odious, or a(n)=0, if there is no such k.

7, 7, 25, 59, 103, 103, 103, 103, 1305, 1305, 10525, 10525, 10525, 25127, 25127, 25127, 106501, 215735, 810163, 810163, 810163, 9554677, 13101403, 13101403, 14299679, 37795511, 37795511, 37795511, 3197105709, 3197105709, 5386711727, 14904706741, 20696039773

Offset: 1

Author

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

Keywords

• nonn
• base

Comments

Conjecture: for all n, a(n) > 0.

Links

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

Crossrefs

Cf. A000069, A001969, A230454, A230495.

Programs

Mathematica

odQ[n_] := OddQ[DigitCount[n, 2, 1]]; odExp[n_] := Module[{e = 1, p = n}, If[odQ[n], While[odQ[p], p *= n; e++]]; e]; seq[nmax_] := Module[{e, emax = 1, n = 3, s = {}}, Do[e = odExp[n]; If[e > emax, s = Join[s, ConstantArray[n, e - emax]]; emax = e], {n, 3, nmax, 2}]; s]; seq[26000] (* Amiram Eldar, Aug 03 2023 *)

Extensions

a(17)-a(22) from Alois P. Heinz, Oct 21 2013

a(23)-a(27) from Peter J. C. Moses, Oct 22 2013

a(28)-a(33) from Amiram Eldar, Aug 03 2023