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A322124
Numbers k such that m = 24k^2 + 4k + 73 and 6m - 5 are both primes.
2
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
OFFSET
1,2
COMMENTS
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, ...
LINKS
Andrzej Rotkiewicz, On some problems of W. Sierpinski, Acta Arithmetica, Vol. 21 (1972), pp. 251-259.
MATHEMATICA
Select[Range[1000], PrimeQ[24#^2 + 4# + 73] && PrimeQ[144#^2 + 24# + 433] &]
PROG
(PARI) isok(n) = isprime(m=24n^2+4n+73) && isprime(6*m-5); \\ Michel Marcus, Nov 28 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 27 2018
STATUS
approved