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A230499 a(n) is the maximal number k of consecutive numbers of the form (2*n-1)*(2*i-1), i=1,2,...,k, which are all evil or all odious (A000069, A001969).

%I A230499 #20 Dec 23 2024 14:53:43
%S A230499 1,3,2,4,4,1,1,9,8,1,1,1,1,1,1,16,16,1,1,1,1,3,4,1,1,3,2,1,1,1,1,33,
%T A230499 32,1,1,1,1,2,2,1,1,2,2,2,2,2,5,1,1,5,2,4,20,4,3,1,1,4,2,1,1,1,1,64,
%U A230499 64,1,1,1,1,2,4,1,1,3,4,5,4,3,2,1,1,2,4,3,3,1,1
%N A230499 a(n) is the maximal number k of consecutive numbers of the form (2*n-1)*(2*i-1), i=1,2,...,k, which are all evil or all odious (A000069, A001969).
%C A230499 We call a(n) the multiplicative index of odious-evil stability of 2*n-1.
%H A230499 Charles R Greathouse IV, <a href="/A230499/b230499.txt">Table of n, a(n) for n = 1..10000</a>
%H A230499 V. Shevelev, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2013-October/author.html">"Odious-evil stability" of integers</a>
%F A230499 If 2*n-1 is Mersenne number (A000225), then a(n)>=n; if 2*n-1 is odious such that 6*n-3 is not in A224072, then a(n)=1.
%e A230499 For n=2, t=2*n-1=3. We see that 3*1=3, 3*3=9,3*5=15 are evil, but 3*7=21 is odious. So, a(2)=3.
%o A230499 (PARI) a(n)=my(t=2*n-1,H=hammingweight(t)%2,i=3); while(H == hammingweight(i*t)%2, i+=2); i\2 \\ _Charles R Greathouse IV_, Oct 22 2013
%Y A230499 Cf. A000069, A001969, A230454, A230495, A230496, A230497, A230498, A000225, A224072.
%K A230499 nonn,base
%O A230499 1,2
%A A230499 _Vladimir Shevelev_, Oct 21 2013
%E A230499 a(17)-a(87) from _Charles R Greathouse IV_, Oct 22 2013