Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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