%I #13 Jul 17 2021 06:56:09

%S 1,3,4,9,11,14,23,36,38,49,66,101,133,134,141,154,158,191,193,196,198,

%T 213,228,241,269,283,294,313,334,339,384,394,411,413,431,453,499,511,

%U 554,558,601,619,639,649,661,686,701,704,718,758,791,804,818,821,881

%N Numbers k such that m = 4k^2 + 2k + 17 and 4m - 3 are both primes.

%C Rotkiewicz proved that if k is in this sequence, and m = 4k^2 + 2k + 17, then m*(4m - 3) is a decagonal Fermat pseudoprime to base 2 (A321870), and thus under Schinzel's Hypothesis H there are infinitely many decagonal Fermat pseudoprimes to base 2.

%C The corresponding pseudoprimes are 2047, 13747, 31417, 514447, 1092547, 2746477, 18985627, 111202297, 137763037, ...

%H Amiram Eldar, <a href="/A321871/b321871.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>.

%e 1 is in the sequence since 4*1^2 + 2*1 + 17 = 23 and 4*23 - 3 = 89 are both primes.

%t Select[Range[1000], PrimeQ[4#^2 + 2# + 17] && PrimeQ[16#^2 + 8# + 65] &]

%o (PARI) isok(n) = isprime(m=4*n^2 + 2*n + 17) && isprime(4*m-3); \\ _Michel Marcus_, Nov 20 2018

%Y Cf. A001107, A001567, A321870.

%K nonn

%O 1,2

%A _Amiram Eldar_, Nov 20 2018