A078654 - OEIS

A078654

a(n) = prime(k) where k = n-th prime congruent to 3 mod 4.

5, 17, 31, 67, 83, 127, 191, 211, 277, 331, 353, 401, 431, 563, 587, 709, 739, 797, 877, 967, 991, 1063, 1153, 1217, 1297, 1409, 1433, 1499, 1597, 1669, 1741, 1847, 2027, 2063, 2221, 2341, 2417, 2477, 2609, 2647, 2897, 3001, 3067, 3109, 3299, 3319, 3407

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = A000040(A002145(n)). [Bruno Berselli, Aug 14 2012]

MATHEMATICA

With[{pc14=Select[Prime[Range[1000]], Mod[#, 4]==3&]}, Flatten[Table[Prime[Take[pc14, {n}]], {n, 100}]]] (* Vincenzo Librandi, Aug 13 2012 *)

PROG

(PARI) tpip(n, m, r) = {sr=0; forprime(x=3, n, if(x%m == r, v=prime(x); sr+=1.0/v; print1(v" "); ) ); print(); print("m="m" r="r" sr="sr); }

(Magma) [NthPrime(n): n in PrimesUpTo(500) | n mod 4 eq 3]; // Bruno Berselli, Aug 14 2012