

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.


1



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
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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. 251259.


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



