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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.

%I A230495 #26 Dec 23 2024 14:53:43
%S A230495 3,3,3,27,287,287,287,287,783,783,783,19099,20249,34391,80577,92589,
%T A230495 211183,211183,211183,1995137,4270443,4270443,4270443,4270443,
%U A230495 17026791,317108969,317108969,317108969,979104339,979104339,6044000725,21911775681,21911775681,26576734759
%N 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.
%C A230495 We conjecture that a(n)>0 for all n.
%H A230495 Vladimir Shevelev, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2013-October/author.html">"Odious-evil stability" of integers</a>, post to the SeqFan Mailing List, Oct 20 2013.
%t A230495 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 *)
%o A230495 (PARI) isevil(n) = (hammingweight(n) % 2) == 0; \\ A000069
%o A230495 isok(k, n) = {if (!isevil(k), return (0)); for (i=1, n, if (!isevil(k^i), return (0));); return (1);}
%o A230495 a(n) = {my(k=1); while(!isok(k,n), k += 2); k;}
%Y A230495 Cf. A000069, A001969, A230454.
%K A230495 nonn,base
%O A230495 1,1
%A A230495 _Vladimir Shevelev_ and _Peter J. C. Moses_, Oct 21 2013
%E A230495 a(26) from _Michel Marcus_, Dec 10 2018
%E A230495 a(27)-a(34) from _Amiram Eldar_, Aug 03 2023