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

1,1

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.

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.

Example

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

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

Crossrefs

Cf. A001652, A002315.

Sequence in context: A296304 A156159 A099011 * A351337 A327652 A112076

Adjacent sequences: A330273 A330274 A330275 * A330277 A330278 A330279

Keyword

nonn

Author

Amiram Eldar, Dec 08 2019

Status

approved