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A087011 Number of primes of form 4*k+3 between n and 2n (inclusive). 3

%I

%S 0,1,1,1,1,2,2,1,1,2,2,2,2,2,2,3,3,3,3,2,2,3,3,3,3,3,3,3,3,4,4,3,3,4,

%T 4,5,5,5,5,6,6,7,7,6,6,6,6,5,5,5,5,6,6,7,7,7,7,7,7,6,6,6,6,7,7,8,8,7,

%U 7,8,8,7,7,7,7,8,8,8,8,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,11,11,11

%N Number of primes of form 4*k+3 between n and 2n (inclusive).

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

%H Amiram Eldar, <a href="/A087011/b087011.txt">Table of n, a(n) for n = 1..10000</a>

%t a[n_] := Module[{c = 0}, Do[If[Mod[k, 4] == 3 && PrimeQ[k], c++], {k, n, 2 n}]; c]; Array[a, 100] (* _Amiram Eldar_, Dec 16 2019 *)

%o (MAGMA) [#[p:p in PrimesInInterval(n,2*n)| p mod 4 eq 3]:n in [1..100]]; // _Marius A. Burtea_, Dec 16 2019

%Y Cf. A035250, A087010, A087012.

%K nonn

%O 1,6

%A _Jason Earls_, Jul 30 2003

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Last modified October 24 10:40 EDT 2021. Contains 348225 sequences. (Running on oeis4.)