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 A087010 Number of primes of form 4*k+1 between n and 2n (inclusive). 3
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 3 16:53 EDT 2023. Contains 363116 sequences. (Running on oeis4.)