A342189 Numbers k such that both k and k+1 are not exponentially 2^n-numbers.

135, 296, 343, 351, 375, 512, 728, 999, 1160, 1215, 1375, 1431, 1592, 1624, 2079, 2240, 2295, 2375, 2456, 2624, 2727, 2888, 2943, 3104, 3159, 3429, 3591, 3624, 3752, 3992, 4023, 4184, 4616, 4671, 4832, 4887, 4913, 5048, 5144, 5319, 5480, 5535, 5696, 5831, 6183

Offset: 1

Author

Amiram Eldar, Mar 04 2021

Keywords

• nonn

Comments

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...

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

cf. A138302.

Similar sequences: A068140, A068781, A342187, A342188.

Programs

Mathematica

exp2nQ[n_] := AllTrue[FactorInteger[n][[;;, 2]], # == 2^IntegerExponent[#, 2] &]; Select[Range[10^4], ! exp2nQ[#] && ! exp2nQ[# + 1] &]