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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).

%I A242281 #25 Jun 25 2025 04:56:15
%S A242281 419,761,911,1601,2351,6269,6551,9029,22259,28559,28949,37139,52571,
%T A242281 56531,67559,70379,78509,108359,114641,133571,135119,138179,146669,
%U A242281 153449,176021,187409,193841,200639,252761,288731,303581,312551,333479,337349,407639,408389
%N 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).
%H A242281 David Radcliffe, <a href="/A242281/b242281.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..675 from Abhiram R Devesh).
%e A242281 a(1): p = 419; 2*p+1 = 839; prime pairs: (419, 73560061) and (839, 590589721).
%e A242281 a(2): p = 761; 2*p+1 = 1523; prime pairs: (761, 440711083) and (1523, 3532642669).
%o A242281 (Python)
%o A242281 from sympy import primerange, isprime
%o A242281 def f(p): return p * p * p + 2
%o A242281 def ok(p): return isprime(2*p+1) and isprime(f(p)) and isprime(f(2*p+1))
%o A242281 print(list(filter(ok, primerange(1_000_000)))) # _David Radcliffe_, Jun 24 2025
%Y A242281 Cf. A048636, A237188, A237256.
%K A242281 nonn
%O A242281 1,1
%A A242281 _Abhiram R Devesh_, May 10 2014