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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.

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%I A230496 #26 Dec 23 2024 14:53:43
%S A230496 7,7,25,59,103,103,103,103,1305,1305,10525,10525,10525,25127,25127,
%T A230496 25127,106501,215735,810163,810163,810163,9554677,13101403,13101403,
%U A230496 14299679,37795511,37795511,37795511,3197105709,3197105709,5386711727,14904706741,20696039773
%N 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.
%C A230496 Conjecture: for all n, a(n) > 0.
%H A230496 Vladimir Shevelev, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2013-October/011792.html">"Odious-evil stability" of integers</a>, post to the SeqFan Mailing List, Oct 20 2013.
%t A230496 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 *)
%Y A230496 Cf. A000069, A001969, A230454, A230495.
%K A230496 nonn,base
%O A230496 1,1
%A A230496 _Vladimir Shevelev_ and _Peter J. C. Moses_, Oct 21 2013
%E A230496 a(17)-a(22) from _Alois P. Heinz_, Oct 21 2013
%E A230496 a(23)-a(27) from _Peter J. C. Moses_, Oct 22 2013
%E A230496 a(28)-a(33) from _Amiram Eldar_, Aug 03 2023