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A330276 NSW pseudoprimes: odd composite numbers k such that A002315((k-1)/2) == 1 (mod k). 7
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 (list; graph; refs; listen; history; text; internal format)
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 * A327652 A112076 A305055

Adjacent sequences:  A330273 A330274 A330275 * A330277 A330278 A330279

KEYWORD

nonn

AUTHOR

Amiram Eldar, Dec 08 2019

STATUS

approved

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Last modified September 17 06:16 EDT 2021. Contains 347478 sequences. (Running on oeis4.)