cp's OEIS Frontend

A084165 Primes which are 1 mod m, where m is the index of the prime in sequence A002313 (Real primes with corresponding complex primes). The index m can be found in A084166 Primes which are -1 mod m can be found in sequence A084163.

%I A084165 #8 Aug 13 2020 12:52:01
%S A084165 5,13,17,37,89,97,181,2689,2969,4621,7457,8081,8161,36709,62701,
%T A084165 169489,169709,169753,282809,770101,5763577,9491101,9491281,9495121,
%U A084165 42544261,115195501,189689041,189689653,312315373,312316409,2294883817
%N A084165 Primes which are 1 mod m, where m is the index of the prime in sequence A002313 (Real primes with corresponding complex primes). The index m can be found in A084166 Primes which are -1 mod m can be found in sequence A084163.
%C A084165 Real primes 2,5,13,17,29,37,... have a unique representation as sum of two squares. Values larger 2 are the primes p with p = 1 mod 4. This is sequence A002313. If p = x^2 + y^2, the corresponding complex prime is x+y*i First complex prime is 1+i with 2 as corresponding real prime, according to reference, page 1-2.
%D A084165 Handbook of First Complex Prime Numbers, Part1 + 2 Ervand Kogbetliantz and Alice Krikorian, Gordon and Breach, 1971
%e A084165 89 is the 11th prime in sequence A002313, 11*8 = 88, so 89 = 1 mod 11
%t A084165 Module[{nn=112*10^6,pr,len},pr=Select[Prime[Range[nn]],MemberQ[ {1,2},Mod[ #,4]]&];len=Length[pr];Select[Thread[{pr,Range[len]}],Mod[ #[[1]],#[[2]]] == 1&]][[All,1]] (* _Harvey P. Dale_, Aug 13 2020 *)
%Y A084165 Cf. A002313, A084163, A084166.
%K A084165 nonn
%O A084165 1,1
%A A084165 _Sven Simon_, May 17 2003