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Numbers k such that 2*k-1 and 2*k+1 are both prime powers (A246655).
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%I #20 Oct 26 2023 06:09:16

%S 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,

%T 114,120,121,135,141,156,174,180,210,216,231,261,285,300,309,321,330,

%U 364,405,411,414,420,429,441,510,516,525,531,546,576,615,639,645,651,660,684

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

%C 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.

%H Jianing Song, <a href="/A365416/b365416.txt">Table of n, a(n) for n = 1..10000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Catalan%27s_conjecture#Pillai&#39;s_conjecture">Catalan's conjecture. Pillai's conjecture</a>.

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

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

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

%Y Cf. A088071, A175593.

%K nonn,easy

%O 1,1

%A _Jianing Song_, Oct 22 2023