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%I #8 Nov 21 2013 13:12:28
%S 1,2,4,7,11,14,16,26,37,44,56,67,76,82,89,91,109,116,121,124,142,146,
%T 149,161,172,179,209,226,247,254,257,259,296,314,319,322,326,329,341,
%U 356,361,362,364,377,391,392,436,439,446,452,467,482,494,496
%N Numbers n such that 4n + 3 and 16n + 15 are prime.
%C Infinite under Dickson's conjecture. [_Charles R Greathouse IV_, Jul 06 2011]
%C No n can be a multiple of 3. If it is 1 mod 3, it cannot end in 3 or 8. If it is 2 mod 3, it cannot end in 1 or 6. One can see the potential of iterative chains producing primes.
%e For n=37, 4*37+3=151 and 16*37+15=607.
%t Select[Range[500], PrimeQ[4# + 3] && PrimeQ[16# + 15] &] (* _Alonso del Arte_, Jul 06 2011 *)
%o (PARI) for(n=1,1e3,if(isprime(4*n+3)&&isprime(16*n+15),print1(n", "))) \\ _Charles R Greathouse IV_, Jul 06 2011
%Y Cf. A002145.
%K nonn
%O 1,2
%A _J. M. Bergot_, Jul 06 2011