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A365411
Numbers k such that 4*k-1 and 4*k+1 are both prime powers (A246655).
2
1, 2, 3, 6, 7, 12, 15, 18, 20, 27, 42, 45, 48, 57, 60, 78, 87, 90, 105, 108, 150, 165, 182, 207, 210, 255, 258, 273, 288, 330, 342, 357, 363, 372, 402, 405, 417, 447, 462, 468, 483, 507, 522, 528, 552, 567, 585, 600, 648, 672, 678, 750, 780, 792, 813, 825, 840, 843
OFFSET
1,2
COMMENTS
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.
LINKS
EXAMPLE
6 is a term since 4*6-1 = 23 is a prime, and 4*6+1 = 25 is a prime power.
PROG
(PARI) isA365411(n) = isprimepower(4*n-1) && isprimepower(4*n+1)
CROSSREFS
Cf. A246655, A366502. Supersequence of A045753.
{2*a(n)} is a subsequence of A365416.
Sequence in context: A130404 A362009 A376313 * A064689 A240175 A238590
KEYWORD
nonn,easy
AUTHOR
Jianing Song, Oct 22 2023
STATUS
approved