A365416 Numbers k such that 2*k-1 and 2*k+1 are both prime powers (A246655).

2, 3, 4, 5, 6, 9, 12, 13, 14, 15, 21, 24, 30, 36, 40, 41, 51, 54, 63, 69, 75, 84, 90, 96, 99, 114, 120, 121, 135, 141, 156, 174, 180, 210, 216, 231, 261, 285, 300, 309, 321, 330, 364, 405, 411, 414, 420, 429, 441, 510, 516, 525, 531, 546, 576, 615, 639, 645, 651, 660, 684

Offset

1,1

Comments

According to Pillai's conjecture, k = 13 is the only term such that 2*k-1 and 2*k+1 both have exponent greater than 1.

Links

Jianing Song, Table of n, a(n) for n = 1..10000

Wikipedia, Catalan's conjecture. Pillai's conjecture.

Example

41 is a term since 2*41-1 = 81 is a prime power, and 2*41+1 = 83 is a prime.

Prog

(PARI) isA365416(n) = isprimepower(2*n-1) && isprimepower(2*n+1)

Crossrefs

Cf. A246655. Supersequence of A040040 and 2*A365411.

Cf. A088071, A175593.

Sequence in context: A325323 A331016 A125155 * A352805 A091179 A036027

Adjacent sequences: A365413 A365414 A365415 * A365417 A365418 A365419

Keyword

nonn,easy

Author

Jianing Song, Oct 22 2023

Status

approved