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%I #16 Jul 17 2021 06:56:41
%S 1,22,25,28,36,42,43,57,63,84,105,127,183,207,211,217,249,259,295,393,
%T 396,417,421,480,508,546,613,624,652,673,760,798,799,816,903,945,963,
%U 1054,1222,1254,1330,1338,1443,1506,1513,1653,1656,1716,1824,1975,2031
%N Numbers k such that m = 24k^2 + 4k + 73 and 6m - 5 are both primes.
%C Rotkiewicz proved that if k is in this sequence, and m = 24k^2 + 4k + 73, then m*(6m - 5) is a tetradecagonal Fermat pseudoprime to base 2 (A322123), and thus under Schinzel's Hypothesis H there are infinitely many tetradecagonal Fermat pseudoprimes to base 2.
%C The corresponding pseudoprimes are 60701, 832127489, 1381243709, 2166133001, 5885873641, 10876592689, 11945978741, ...
%H Amiram Eldar, <a href="/A322124/b322124.txt">Table of n, a(n) for n = 1..10000</a>
%H Andrzej Rotkiewicz, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa21/aa21137.pdf">On some problems of W. Sierpinski</a>, Acta Arithmetica, Vol. 21 (1972), pp. 251-259.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Schinzel%27s_hypothesis_H">Schinzel's Hypothesis H</a>.
%t Select[Range[1000], PrimeQ[24#^2 + 4# + 73] && PrimeQ[144#^2 + 24# + 433] &]
%o (PARI) isok(n) = isprime(m=24n^2+4n+73) && isprime(6*m-5); \\ _Michel Marcus_, Nov 28 2018
%Y Cf. A001567, A051866, A322123.
%K nonn
%O 1,2
%A _Amiram Eldar_, Nov 27 2018
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