A367695 Numbers k such that k and k+1 are both exponentially odd numbers (A268335).

1, 2, 5, 6, 7, 10, 13, 14, 21, 22, 23, 26, 29, 30, 31, 32, 33, 34, 37, 38, 39, 40, 41, 42, 46, 53, 54, 55, 56, 57, 58, 61, 65, 66, 69, 70, 73, 77, 78, 82, 85, 86, 87, 88, 93, 94, 95, 96, 101, 102, 103, 104, 105, 106, 109, 110, 113, 114, 118, 119, 122, 127, 128

Offset: 1

Author

Amiram Eldar, Nov 27 2023

Keywords

• nonn

Comments

The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 6, 48, 478, 4734, 47195, 471707, 4716892, 47168363, 471681183, 4716806520, ... . Apparently, the asymptotic density of this sequence exists and equals Product_{p prime} (1 - 2/(p*(p+1))) = 0.47168... (A307868).

Links

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

Crossrefs

Subsequence of A268335.

Cf. A307868.

Subsequences: A007674, A325058.

Similar sequences: A071318, A121495, A340152, A367696.

Programs

Mathematica

expOddQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], OddQ]; Select[Range[128], And @@ expOddQ /@ {#, # + 1} &]

PARI

isexpodd(n) = {my(f = factor(n)); for(i=1, #f~, if (!(f[i, 2] % 2), return (0))); 1;}
is(n) = isexpodd(n) && isexpodd(n+1)