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A367695
Numbers k such that k and k+1 are both exponentially odd numbers (A268335).
3
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
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 27 2023
STATUS
approved