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 A171833 Pythagorean primes with Pythagorean prime index. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified June 25 04:06 EDT 2019. Contains 324345 sequences. (Running on oeis4.)