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

1,9

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

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 *)

Prog

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

Crossrefs

Cf. A035250, A087011, A087012.

Sequence in context: A102300 A359511 A202146 * A098220 A297032 A346953

Adjacent sequences: A087007 A087008 A087009 * A087011 A087012 A087013

Keyword

nonn

Author

Jason Earls, Jul 30 2003

Status

approved