OFFSET
1,1
COMMENTS
Rotkiewicz proved that if k is in this sequence then (4k + 1)*(8k + 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. 251-259.
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
(Python)
from sympy import isprime
def ok(n): return isprime(4*n + 1) and isprime(8*n + 1)
print(list(filter(ok, range(1558)))) # Michael S. Branicky, Sep 24 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 20 2018
STATUS
approved