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A321867 Numbers n such that 8n+1, 12n+1 and 24n+1 are primes and the last two are also of the form x^2 + 27y^2, so the tetrahedral number T(24n+1) is a Fermat pseudoprime to base 2. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The first 3 terms were found by Rotkiewicz.

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

LINKS

Table of n, a(n) for n=1..38.

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

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Last modified March 22 12:39 EDT 2019. Contains 321421 sequences. (Running on oeis4.)