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A321869 Numbers n such that m = 3n^2 + 2n + 10 and 3m - 2 are both primes. 1
3, 9, 17, 57, 69, 177, 293, 303, 317, 339, 377, 407, 429, 437, 443, 467, 503, 573, 597, 759, 783, 797, 849, 897, 1329, 1343, 1409, 1899, 1923, 2267, 2357, 2427, 2579, 2679, 2739, 2843, 2967, 3089, 3263, 3279, 3303, 3323, 3419, 3459, 3509, 3933, 3999, 4293 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Rotkiewicz proved that if n is in this sequence, and m = 3n^2 + 2n + 10, then m*(3m - 2) is an octagonal Fermat pseudoprime to base 2 (A321868), and thus under Schinzel's Hypothesis H there are infinitely many octagonal Fermat pseudoprimes to base 2.

The corresponding pseudoprimes are 467285, 1532245, 20134661, 26190165, 52685061, 95519061, ...

LINKS

Table of n, a(n) for n=1..48.

Andrzej Rotkiewicz, On some problems of W. Sierpinski, Acta Arithmetica, Vol. 21 (1972), pp. 251-259.

Wikipedia, Schinzel's Hypothesis H.

EXAMPLE

3 is in the sequence since 3*3^2 + 2*3 + 10 = 43 and 3*43 - 2 = 127 are both primes.

MATHEMATICA

Select[Range[1000], PrimeQ[3#^2 + 2# + 10] && PrimeQ[9#^2 + 6# + 28]  &]

PROG

(PARI) isok(n) = isprime(m=3*n^2 + 2*n + 10) && isprime(3*m-2); \\ Michel Marcus, Nov 20 2018

CROSSREFS

Cf. A000567, A001567, A321868.

Sequence in context: A173140 A018307 A108050 * A009211 A105538 A056404

Adjacent sequences:  A321866 A321867 A321868 * A321870 A321871 A321872

KEYWORD

nonn

AUTHOR

Amiram Eldar, Nov 20 2018

STATUS

approved

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Last modified April 25 23:48 EDT 2019. Contains 322465 sequences. (Running on oeis4.)