

A330276


NSW pseudoprimes: odd composite numbers k such that A002315((k1)/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
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OFFSET

1,1


COMMENTS

If p is an odd prime, then A002315((p1)/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((k1)/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. 129140.


EXAMPLE

169 = 13^2 is a term since it is composite and A002315((1691)/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



