A087010 Number of primes of form 4*k+1 between n and 2n (inclusive).

0, 0, 1, 1, 1, 0, 1, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 4, 3, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 5, 6, 6, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 8, 9, 9, 9, 9, 9, 9, 10, 9, 10, 10, 10, 9, 9

Offset: 1

Author

Jason Earls, Jul 30 2003

Keywords

• nonn

Comments

Erdős proved that between any n > 7 and its double there are always at least two primes, one of form 4*k+1 and one of form 4*k+3.

References

• B. Schechter, "My Brain is Open: The Mathematical Journeys of Paul Erdős," Simon & Schuster, New York, 1998, p. 62.

Links

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

Crossrefs

Cf. A035250, A087011, A087012.

Programs

Magma

[#[p:p in PrimesInInterval(n,2*n)| p mod 4 eq 1]:n in [1..110]]; // Marius A. Burtea, Dec 16 2019

Mathematica

a[n_] := Module[{c = 0}, Do[If[Mod[k, 4] == 1 && PrimeQ[k], c++], {k, n, 2 n}]; c]; Array[a, 100] (* Amiram Eldar, Dec 16 2019 *)