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

Author

Amiram Eldar, Nov 27 2018

Keywords

• nonn

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.

Crossrefs

Cf. A001567, A051866, A322123.

Programs

Mathematica

Select[Range[1000], PrimeQ[24#^2 + 4# + 73] && PrimeQ[144#^2 + 24# + 433]  &]

PARI

isok(n) = isprime(m=24n^2+4n+73) && isprime(6*m-5); \\ Michel Marcus, Nov 28 2018