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Numbers k such that 4*k-1 and 4*k+1 are both prime powers (A246655).
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%I #21 Oct 23 2023 02:09:46

%S 1,2,3,6,7,12,15,18,20,27,42,45,48,57,60,78,87,90,105,108,150,165,182,

%T 207,210,255,258,273,288,330,342,357,363,372,402,405,417,447,462,468,

%U 483,507,522,528,552,567,585,600,648,672,678,750,780,792,813,825,840,843

%N Numbers k such that 4*k-1 and 4*k+1 are both prime powers (A246655).

%C Let b(q) be the number of pairs of consecutive nonzero squares in the finite field F_q for odd prime powers q, then b(q) = b(q') for q < q' if and only if q = 4*k-1 and q' = 4*k+1 for k being a term of this sequence, in which case we have b(q) = b(q') = k-1.

%H Jianing Song, <a href="/A365411/b365411.txt">Table of n, a(n) for n = 1..10000</a>

%e 6 is a term since 4*6-1 = 23 is a prime, and 4*6+1 = 25 is a prime power.

%o (PARI) isA365411(n) = isprimepower(4*n-1) && isprimepower(4*n+1)

%Y Cf. A246655, A366502. Supersequence of A045753.

%Y {2*a(n)} is a subsequence of A365416.

%K nonn,easy

%O 1,2

%A _Jianing Song_, Oct 22 2023