This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A342189 #8 Mar 06 2021 06:00:06 %S A342189 135,296,343,351,375,512,728,999,1160,1215,1375,1431,1592,1624,2079, %T A342189 2240,2295,2375,2456,2624,2727,2888,2943,3104,3159,3429,3591,3624, %U A342189 3752,3992,4023,4184,4616,4671,4832,4887,4913,5048,5144,5319,5480,5535,5696,5831,6183 %N A342189 Numbers k such that both k and k+1 are not exponentially 2^n-numbers. %C A342189 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 A342189 Amiram Eldar, <a href="/A342189/b342189.txt">Table of n, a(n) for n = 1..10000</a> %e A342189 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 A342189 exp2nQ[n_] := AllTrue[FactorInteger[n][[;;, 2]], # == 2^IntegerExponent[#, 2] &]; Select[Range[10^4], ! exp2nQ[#] && ! exp2nQ[# + 1] &] %Y A342189 cf. A138302. %Y A342189 Similar sequences: A068140, A068781, A342187, A342188. %K A342189 nonn %O A342189 1,1 %A A342189 _Amiram Eldar_, Mar 04 2021