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

1,2

Links

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

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 *)

Prog

(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
(Magma) f:=func<n, r|#[p:p in PrimesInInterval(n, 2*n)| p mod 4 eq r]>; [k:k in [1..250]|f(k, 1) eq f(k, 3)]; // Marius A. Burtea, Dec 16 2019

Crossrefs

Cf. A035250, A087010, A087011.

Sequence in context: A346456 A001602 A308197 * A047366 A184776 A202104

Adjacent sequences: A087009 A087010 A087011 * A087013 A087014 A087015

Keyword

nonn

Author

Jason Earls, Jul 30 2003

Status

approved