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

1,2

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

Mathematica

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

Prog

(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)

Crossrefs

Subsequence of A268335.

Cf. A307868.

Subsequences: A007674, A325058.

Similar sequences: A071318, A121495, A340152, A367696.

Sequence in context: A050002 A047578 A259605 * A372690 A284393 A287366

Adjacent sequences: A367692 A367693 A367694 * A367696 A367697 A367698

Keyword

nonn

Author

Amiram Eldar, Nov 27 2023

Status

approved