cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A087010 #17 Sep 08 2022 08:45:11
%S A087010 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,
%T A087010 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,
%U A087010 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
%N A087010 Number of primes of form 4*k+1 between n and 2n (inclusive).
%C A087010 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.
%D A087010 B. Schechter, "My Brain is Open: The Mathematical Journeys of Paul Erdős," Simon & Schuster, New York, 1998, p. 62.
%H A087010 Amiram Eldar, <a href="/A087010/b087010.txt">Table of n, a(n) for n = 1..10000</a>
%t A087010 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 *)
%o A087010 (Magma) [#[p:p in PrimesInInterval(n,2*n)| p mod 4 eq 1]:n in [1..110]]; // _Marius A. Burtea_, Dec 16 2019
%Y A087010 Cf. A035250, A087011, A087012.
%K A087010 nonn
%O A087010 1,9
%A A087010 _Jason Earls_, Jul 30 2003