A087012 Numbers m such that the number of primes of form 4*k+1 between m and 2*m equals the number of primes of form 4*k+3 between m and 2*m (inclusive).

1, 3, 4, 5, 8, 10, 11, 12, 13, 15, 20, 22, 23, 24, 25, 26, 31, 34, 35, 37, 49, 50, 52, 53, 57, 58, 59, 62, 63, 69, 72, 73, 75, 79, 82, 83, 84, 85, 86, 91, 92, 93, 94, 95, 97, 99, 141, 147, 148, 149, 152, 153, 164, 165, 168, 175, 176, 182, 183, 187, 188, 189, 200, 244, 245

Offset: 1

Author

Jason Earls, Jul 30 2003

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A035250, A087010, A087011.

Programs

Magma

f:=func; [k:k in [1..250]|f(k,1) eq f(k,3)]; // Marius A. Burtea, Dec 16 2019

Mathematica

seqQ[n_] := Module[{c1 = 0, c3 = 0}, Do[If[Mod[k, 4] == 1 && PrimeQ[k], c1++]; If[Mod[k, 4] == 3 && PrimeQ[k], c3++], {k, n, 2 n}]; c1 == c3]; Select[Range[250], seqQ] (* Amiram Eldar, Dec 16 2019 *)
npfQ[n_]:=With[{prs=Select[Range[n,2n],PrimeQ]},Length[Select[prs,Mod[#,4]==1&]]==Length[Select[prs,Mod[#,4]==3&]]]; Select[ Range[ 250],npfQ] (* Harvey P. Dale, Sep 25 2024 *)

PARI

for(m=1,250,my(k1=0,k3=0);forprime(p=m,2*m,if(p%4==1,k1++);if(p%4==3,k3++));if(k1==k3,print1(m," "))) \\ Hugo Pfoertner, Dec 16 2019