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%I #13 Jul 24 2019 09:46:13
%S 1,46,58,133,145,175,208,223,241,403,430,463,526,568,808,868,985,1015,
%T 1021,1105,1120,1360,1465,1501,1600,1918,1978,2236,2350,2413,2908,
%U 2965,3043,3211,3265,3523,3556,3568,3601,3721,3811,3868,4066,4291,4300,4336,4831
%N Numbers k such that m = 8k^2 + 2k + 33 and 8m - 7 are both primes.
%C Rotkiewicz proved that if k is in this sequence, and m = 8k^2 + 2k + 33, then m*(8m - 7) is an octadecagonal Fermat pseudoprime to base 2 (A322160), and thus under Schinzel's Hypothesis H there are infinitely many decagonal Fermat pseudoprimes to base 2.
%C The corresponding pseudoprimes are 14491, 2326319101, 5858192341, 160881885091, 227198832571, 481700815831, 960833787841, ...
%H Amiram Eldar, <a href="/A322161/b322161.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 8*1^2 + 2*1 + 33 = 43 and 8*43 - 7 = 337 are both primes.
%t Select[Range[1000], PrimeQ[8#^2 + 2# + 33] && PrimeQ[64#^2 + 16# + 257] &]
%o (PARI) isok(n) = isprime(m = 8*n^2+2*n+33) && isprime(8*m-7); \\ _Michel Marcus_, Nov 29 2018
%Y Cf. A001567, A051870, A322160.
%K nonn
%O 1,2
%A _Amiram Eldar_, Nov 29 2018
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