A171833 Pythagorean primes with Pythagorean prime index.

37, 109, 157, 293, 397, 433, 613, 709, 877, 1097, 1213, 1249, 1381, 1453, 1861, 2029, 2141, 2381, 2521, 2713, 2753, 3301, 3373, 3517, 3761, 3989, 4129, 4177, 4357, 4729, 4801, 5189, 5393, 5441, 5801, 6101, 6229, 6301, 6397, 6637, 6829, 7129, 7309, 7369

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..44.

Formula

a(n) = A002144(A002144(n)).

Example

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.

Mathematica

A002144=Select[Range[5, 100000, 4], PrimeQ];
Table[A002144[[A002144[[n]]]], {n, 300}] (* Zak Seidov, Jul 22 2010 *)

Prog

(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

Crossrefs

Cf. A000040, A002144, A006450.

Sequence in context: A139934 A142051 A282852 * A257117 A033215 A195316

Adjacent sequences: A171830 A171831 A171832 * A171834 A171835 A171836

Keyword

easy,nonn

Author

Jonathan Vos Post, Dec 19 2009

Extensions

More terms from Max Alekseyev, Feb 08 2010

Status

approved