A321867 Numbers k such that 8k+1, 12k+1 and 24k+1 are primes and the last two are also of the form x^2 + 27y^2, so the tetrahedral number T(24k+1) is a Fermat pseudoprime to base 2.

1179, 1274, 1895, 4775, 5304, 5874, 6525, 6639, 13035, 16380, 17424, 18459, 21239, 21584, 21714, 22475, 22715, 22734, 27410, 28304, 29340, 29909, 31755, 32294, 34700, 37700, 41525, 42164, 42929, 42950, 43275, 46415, 47174, 47300, 53364, 57879, 59739, 61194

Offset

1,1

Comments

The first 3 terms were found by Rotkiewicz.

The generated tetrahedral pseudoprimes are 3776730328549, 4765143438329, 15680770945781, ...

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.

Example

1179 is in the sequence since 8*1179+1 = 9433, 12*1179+1 = 14149 = 107^2 + 27*10^2 and 24*1179+1 = 28297 = 163^2 + 27*8^2 are primes.

Mathematica

sqQ[n_] := n>0 && IntegerQ[Sqrt[n]]; sqsumQ[n_] := PrimeQ[n] && False =!= Reduce[ x^2 + 27 y^2 == n, {x, y}, Integers]; aQ[n_] := PrimeQ[8n+1] && sqsumQ[12n+1] && sqsumQ[24n+1]; Select[Range[100000], aQ]

Crossrefs

Cf. A000292, A001567, A014752, A321866.

Sequence in context: A270114 A258912 A237094 * A210847 A320716 A269017

Adjacent sequences: A321864 A321865 A321866 * A321868 A321869 A321870

Keyword

nonn

Author

Amiram Eldar, Nov 20 2018

Status

approved