A242281 Smaller member of a Sophie Germain pair in which each member of the pair is the smaller of its prime pair (p, (p*p*p)+2).

419, 761, 911, 1601, 2351, 6269, 6551, 9029, 22259, 28559, 28949, 37139, 52571, 56531, 67559, 70379, 78509, 108359, 114641, 133571, 135119, 138179, 146669, 153449, 176021, 187409, 193841, 200639, 252761, 288731, 303581, 312551, 333479, 337349, 407639, 408389

Offset: 1

Author

Abhiram R Devesh, May 10 2014

Keywords

• nonn

Examples

			a(1): p = 419; 2*p+1 = 839; prime pairs: (419, 73560061) and (839, 590589721).
a(2): p = 761; 2*p+1 = 1523; prime pairs: (761, 440711083) and (1523, 3532642669).
		

Links

• David Radcliffe, Table of n, a(n) for n = 1..10000 (terms 1..675 from Abhiram R Devesh).

Crossrefs

Cf. A048636, A237188, A237256.

Programs

Python

from sympy import primerange, isprime
def f(p): return p * p * p + 2
def ok(p): return isprime(2*p+1) and isprime(f(p)) and isprime(f(2*p+1))
print(list(filter(ok, primerange(1_000_000)))) # David Radcliffe, Jun 24 2025