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 A321869 Numbers n such that m = 3n^2 + 2n + 10 and 3m - 2 are both primes. 1
 3, 9, 17, 57, 69, 177, 293, 303, 317, 339, 377, 407, 429, 437, 443, 467, 503, 573, 597, 759, 783, 797, 849, 897, 1329, 1343, 1409, 1899, 1923, 2267, 2357, 2427, 2579, 2679, 2739, 2843, 2967, 3089, 3263, 3279, 3303, 3323, 3419, 3459, 3509, 3933, 3999, 4293 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Rotkiewicz proved that if n is in this sequence, and m = 3n^2 + 2n + 10, then m*(3m - 2) is an octagonal Fermat pseudoprime to base 2 (A321868), and thus under Schinzel's Hypothesis H there are infinitely many octagonal Fermat pseudoprimes to base 2. The corresponding pseudoprimes are 467285, 1532245, 20134661, 26190165, 52685061, 95519061, ... LINKS Andrzej Rotkiewicz, On some problems of W. Sierpinski, Acta Arithmetica, Vol. 21 (1972), pp. 251-259. Wikipedia, Schinzel's Hypothesis H. EXAMPLE 3 is in the sequence since 3*3^2 + 2*3 + 10 = 43 and 3*43 - 2 = 127 are both primes. MATHEMATICA Select[Range[1000], PrimeQ[3#^2 + 2# + 10] && PrimeQ[9#^2 + 6# + 28]  &] PROG (PARI) isok(n) = isprime(m=3*n^2 + 2*n + 10) && isprime(3*m-2); \\ Michel Marcus, Nov 20 2018 CROSSREFS Cf. A000567, A001567, A321868. Sequence in context: A173140 A018307 A108050 * A009211 A105538 A056404 Adjacent sequences:  A321866 A321867 A321868 * A321870 A321871 A321872 KEYWORD nonn AUTHOR Amiram Eldar, Nov 20 2018 STATUS approved

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Last modified April 25 23:48 EDT 2019. Contains 322465 sequences. (Running on oeis4.)