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A321869
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Numbers k such that m = 3k^2 + 2k + 10 and 3m - 2 are both primes.
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2
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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
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OFFSET
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1,1
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COMMENTS
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Rotkiewicz proved that if k is in this sequence, and m = 3k^2 + 2k + 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, ...
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LINKS
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EXAMPLE
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3 is in the sequence since 3*3^2 + 2*3 + 10 = 43 and 3*43 - 2 = 127 are both primes.
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MATHEMATICA
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Select[Range[1000], PrimeQ[3#^2 + 2# + 10] && PrimeQ[9#^2 + 6# + 28] &]
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PROG
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(PARI) isok(n) = isprime(m=3*n^2 + 2*n + 10) && isprime(3*m-2); \\ Michel Marcus, Nov 20 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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