A330276 NSW pseudoprimes: odd composite numbers k such that A002315((k-1)/2) == 1 (mod k).

169, 385, 961, 1105, 1121, 3827, 4901, 6265, 6441, 6601, 7107, 7801, 8119, 10945, 11285, 13067, 15841, 18241, 19097, 20833, 24727, 27971, 29953, 31417, 34561, 35459, 37345, 37505, 38081, 39059, 42127, 45451, 45961, 47321, 49105, 52633, 53041, 55969, 56953, 58241

Offset: 1

Author

Amiram Eldar, Dec 08 2019

Keywords

• nonn

Comments

If p is an odd prime, then A002315((p-1)/2) == 1 (mod p). This sequence consists of the odd composite numbers for which this congruence holds.

Equivalently, odd composite numbers k such that A001652((k-1)/2) is divisible by k.

Examples

			169 = 13^2 is a term since it is composite and A002315((169-1)/2) - 1 = A002315(84) - 1 is divisible by 169.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000
• Morris Newman, Daniel Shanks, and H. C. Williams, Simple groups of square order and an interesting sequence of primes, Acta Arithmetica, Vol. 38, No. 2 (1980), pp. 129-140.

Crossrefs

Cf. A001652, A002315.

Programs

Mathematica

a0 = 1; a1 = 7; k = 5; seq = {}; Do[a = 6 a1 - a0; a0 = a1; a1 = a; If[CompositeQ[k] && Divisible[a - 1, k], AppendTo[seq, k]]; k += 2, {n, 2, 10^4}]; seq