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%I #9 Nov 27 2023 09:47:07
%S 1,2,3,4,5,6,9,10,11,12,13,14,15,16,17,18,19,20,21,22,25,28,29,30,33,
%T 34,35,36,37,38,41,42,43,44,45,46,47,48,49,50,51,52,57,58,59,60,61,62,
%U 65,66,67,68,69,70,73,74,75,76,77,78,79,80,81,82,83,84,85
%N Numbers k such that k and k+1 are both exponentially odious numbers (A270428).
%C The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 8, 78, 762, 7615, 76113, 761127, 7611222, 76111895, 761119135, 7611190807, ... . Apparently, the asymptotic density of this sequence exists and equals 0.761119... .
%H Amiram Eldar, <a href="/A367696/b367696.txt">Table of n, a(n) for n = 1..10000</a>
%t expOdQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], OddQ[DigitCount[#, 2, 1]] &]; Select[Range[100], And @@ expOdQ /@ {#, # + 1} &]
%o (PARI) isexpod(n) = {my(f = factor(n)); for(i=1, #f~, if (!(hammingweight(f[i, 2]) % 2), return (0))); 1;}
%o is(n) = isexpod(n) && isexpod(n+1)
%Y Subsequence of A270428.
%Y Subsequences: A007674, A367697.
%Y Similar sequences: A071318, A121495, A340152, A367695.
%K nonn,base
%O 1,2
%A _Amiram Eldar_, Nov 27 2023
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