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%I #10 Feb 03 2018 09:53:59
%S 37,109,157,293,397,433,613,709,877,1097,1213,1249,1381,1453,1861,
%T 2029,2141,2381,2521,2713,2753,3301,3373,3517,3761,3989,4129,4177,
%U 4357,4729,4801,5189,5393,5441,5801,6101,6229,6301,6397,6637,6829,7129,7309,7369
%N Pythagorean primes with Pythagorean prime index.
%C This is to Pythagorean primes (A002144), primes of the form 4n+1, as primes with prime subscripts (A006450) is to primes (A000040). Hence this is one of four related sequences into which every prime with prime subscripts (A006450) may be classified: Pythagorean primes (A002144) with Pythagorean prime index; Pythagorean primes (A002144) whose indices are of the form 4n+3 (A002145); primes of the form 4n+3 with Pythagorean prime index; and primes of the form 4n+3 whose indices are primes of form 4n+3.
%F a(n) = A002144(A002144(n)).
%e a(1) = 37 because the smallest prime of form 4n+1 is 4*1+1 = 5, and the fifth prime of the form 4n+1 is 4*9+1 = 37. a(2) = 109 because the second smallest prime of form 4n+1 is 4*3+1 = 13, and the thirteenth prime of the form 4n+1 is 4*27+1 = 109.
%t A002144=Select[Range[5,100000,4],PrimeQ];
%t Table[A002144[[A002144[[n]]]],{n,300}] (* _Zak Seidov_, Jul 22 2010 *)
%o (PARI) c=0; forprime(p=2,10^5, if(p%4==1,c++; if(isprime(c)&&c%4==1,print1(p,", ")))) \\ _Max Alekseyev_, Feb 08 2010
%Y Cf. A000040, A002144, A006450.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Dec 19 2009
%E More terms from _Max Alekseyev_, Feb 08 2010
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