Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #19 Sep 08 2022 08:45:08
%S 11,41,59,109,157,179,241,283,367,461,509,547,599,617,773,859,919,
%T 1031,1087,1171,1201,1447,1471,1523,1621,1723,1787,1823,1913,2081,
%U 2099,2269,2351,2381,2549,2683,2719
%N a(n) = prime(k) where k = n-th prime congruent to 1 mod 4.
%C Sum 1/a(n) appears to converge albeit slowly.
%H Vincenzo Librandi, <a href="/A078653/b078653.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = A000040(A002144(n)). [_Bruno Berselli_, Aug 14 2012]
%t With[{pc14=Select[Prime[Range[100]],Mod[#,4]==1&]},Flatten[Table[ Prime[ Take[ pc14,{n}]],{n,40}]]] (* _Harvey P. Dale_, Aug 12 2011 *)
%o (PARI) pip(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); }
%o (Magma) [NthPrime(n): n in PrimesUpTo(400) | n mod 4 eq 1]; // _Bruno Berselli_, Aug 14 2012
%Y Cf. A006450, A078654.
%K nonn,easy
%O 1,1
%A _Cino Hilliard_, Dec 14 2002
%E Offset changed from 0 to 1 by _Vincenzo Librandi_, Aug 14 2012