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%I #8 Mar 06 2021 06:00:06
%S 135,296,343,351,375,512,728,999,1160,1215,1375,1431,1592,1624,2079,
%T 2240,2295,2375,2456,2624,2727,2888,2943,3104,3159,3429,3591,3624,
%U 3752,3992,4023,4184,4616,4671,4832,4887,4913,5048,5144,5319,5480,5535,5696,5831,6183
%N Numbers k such that both k and k+1 are not exponentially 2^n-numbers.
%C The numbers of terms not exceeding 10^k for k = 3, 4, ..., are 8, 76, 775, 7776, 77845, 778303, 7783285, 77832769, ... Apparently this sequence has an asymptotic density 0.0077832...
%H Amiram Eldar, <a href="/A342189/b342189.txt">Table of n, a(n) for n = 1..10000</a>
%e 135 is a term since 135 = 3^3 * 5 and 136 = 2^3 * 17 both have an exponent in their prime factorization which is not a power of 2.
%t exp2nQ[n_] := AllTrue[FactorInteger[n][[;;, 2]], # == 2^IntegerExponent[#, 2] &]; Select[Range[10^4], ! exp2nQ[#] && ! exp2nQ[# + 1] &]
%Y cf. A138302.
%Y Similar sequences: A068140, A068781, A342187, A342188.
%K nonn
%O 1,1
%A _Amiram Eldar_, Mar 04 2021