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