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A322124
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Numbers k such that m = 24k^2 + 4k + 73 and 6m - 5 are both primes.
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2
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1, 22, 25, 28, 36, 42, 43, 57, 63, 84, 105, 127, 183, 207, 211, 217, 249, 259, 295, 393, 396, 417, 421, 480, 508, 546, 613, 624, 652, 673, 760, 798, 799, 816, 903, 945, 963, 1054, 1222, 1254, 1330, 1338, 1443, 1506, 1513, 1653, 1656, 1716, 1824, 1975, 2031
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OFFSET
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1,2
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COMMENTS
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Rotkiewicz proved that if k is in this sequence, and m = 24k^2 + 4k + 73, then m*(6m - 5) is a tetradecagonal Fermat pseudoprime to base 2 (A322123), and thus under Schinzel's Hypothesis H there are infinitely many tetradecagonal Fermat pseudoprimes to base 2.
The corresponding pseudoprimes are 60701, 832127489, 1381243709, 2166133001, 5885873641, 10876592689, 11945978741, ...
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LINKS
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MATHEMATICA
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Select[Range[1000], PrimeQ[24#^2 + 4# + 73] && PrimeQ[144#^2 + 24# + 433] &]
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PROG
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(PARI) isok(n) = isprime(m=24n^2+4n+73) && isprime(6*m-5); \\ Michel Marcus, Nov 28 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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