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A330276 NSW pseudoprimes: odd composite numbers k such that A002315((k-1)/2) == 1 (mod k). 7

%I

%S 169,385,961,1105,1121,3827,4901,6265,6441,6601,7107,7801,8119,10945,

%T 11285,13067,15841,18241,19097,20833,24727,27971,29953,31417,34561,

%U 35459,37345,37505,38081,39059,42127,45451,45961,47321,49105,52633,53041,55969,56953,58241

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

%C 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.

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

%H Amiram Eldar, <a href="/A330276/b330276.txt">Table of n, a(n) for n = 1..1000</a>

%H Morris Newman, Daniel Shanks, and H. C. Williams, <a href="https://eudml.org/doc/205728">Simple groups of square order and an interesting sequence of primes</a>, Acta Arithmetica, Vol. 38, No. 2 (1980), pp. 129-140.

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

%t 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

%Y Cf. A001652, A002315.

%K nonn

%O 1,1

%A _Amiram Eldar_, Dec 08 2019

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Last modified October 15 16:57 EDT 2021. Contains 348033 sequences. (Running on oeis4.)