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

Author

Jianing Song, Oct 22 2023

Keywords

• nonn
• easy

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.

Examples

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

Links

• Jianing Song, Table of n, a(n) for n = 1..10000
• Wikipedia, Catalan's conjecture. Pillai's conjecture.

Crossrefs

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

Cf. A088071, A175593.

Programs

PARI

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