A365411 Numbers k such that 4*k-1 and 4*k+1 are both prime powers (A246655).

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

Author

Jianing Song, Oct 22 2023

Keywords

• nonn
• easy

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.

Examples

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

Links

• Jianing Song, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A246655, A366502. Supersequence of A045753.

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

Programs

PARI

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