A322124 Numbers k such that m = 24k^2 + 4k + 73 and 6m - 5 are both primes.

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

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: A345479 A295799 A338603 * A178423 A108632 A045096

Adjacent sequences: A322121 A322122 A322123 * A322125 A322126 A322127

Keyword

nonn

Author

Amiram Eldar, Nov 27 2018

Status

approved