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A322124 Numbers n such that m = 24n^2 + 4n + 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Rotkiewicz proved that if n is in this sequence, and m = 24n^2 + 4n + 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

Amiram Eldar, Table of n, a(n) for n = 1..10000

Andrzej Rotkiewicz, On some problems of W. Sierpinski, Acta Arithmetica, Vol. 21 (1972), pp. 251-259.

Wikipedia, Schinzel's Hypothesis H.

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

Cf. A001567, A051866, A322123.

Sequence in context: A070809 A280646 A295799 * A178423 A108632 A045096

Adjacent sequences:  A322121 A322122 A322123 * A322125 A322126 A322127

KEYWORD

nonn

AUTHOR

Amiram Eldar, Nov 27 2018

STATUS

approved

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Last modified August 8 14:36 EDT 2020. Contains 336298 sequences. (Running on oeis4.)