

A320599


Numbers n such that 4n + 1 and 8n + 1 are both primes.


2



9, 24, 39, 57, 84, 144, 150, 165, 207, 219, 234, 249, 252, 267, 309, 324, 357, 402, 414, 507, 522, 534, 555, 570, 639, 654, 759, 765, 777, 792, 795, 882, 924, 927, 942, 969, 1044, 1065, 1089, 1155, 1200, 1215, 1227, 1389, 1395, 1437, 1509, 1530, 1554, 1557
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OFFSET

1,1


COMMENTS

Rotkiewicz proved that if n is in this sequence then (4n + 1)(8n + 1) is a triangular Fermat pseudoprime to base 2 (A293622), and thus under Schinzel's Hypothesis H there are infinitely many triangular Fermat pseudoprimes to base 2.
The corresponding pseudoprimes are 2701, 18721, 49141, 104653, 226801, 665281, 721801, ...


LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000
Andrzej Rotkiewicz, On some problems of W. Sierpinski, Acta Arithmetica, Vol. 21 (1972), pp. 251259.
Wikipedia, Schinzel's Hypothesis H.


EXAMPLE

9 is in the sequence since 4*9 + 1 = 37 and 8*9 + 1 = 73 are both primes.


MATHEMATICA

Select[Range[1000], PrimeQ[4#+1] && PrimeQ[8#+1] &]


PROG

(PARI) isok(n) = isprime(4*n+1) && isprime(8*n+1); \\ Michel Marcus, Nov 20 2018


CROSSREFS

Cf. A000217, A001567, A293622.
Sequence in context: A121453 A003343 A047720 * A293846 A212462 A161449
Adjacent sequences: A320596 A320597 A320598 * A320600 A320601 A320602


KEYWORD

nonn


AUTHOR

Amiram Eldar, Nov 20 2018


STATUS

approved



