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.

Showing 1-3 of 3 results.

A084297 Primes p=prime(m) such that pi(m*p)/m is an integer.

Original entry on oeis.org

2, 5, 211, 457, 1223, 3943, 130259, 167953, 468473, 721159, 927317, 2026061, 7066487
Offset: 1

Views

Author

Labos Elemer, May 27 2003

Keywords

Crossrefs

Cf. A000040, A000720, A057855, A084295.

Programs

  • Mathematica
    Do[s=PrimePi[n*Prime[n]]/n; If[IntegerQ[s], Print[Prime[n]]], {n, 1, 100000}]

Formula

a(n) = prime(A084295(n)).

Extensions

Name edited by Michel Marcus, Aug 30 2019
a(9)-a(12) from Giovanni Resta, Sep 02 2019
a(13) from Chai Wah Wu, May 14 2020

A084298 Integer quotients pi(m*prime(m))/m.

Original entry on oeis.org

1, 2, 26, 48, 108, 292, 6471, 8147, 20745, 30803, 38806, 79760, 254050
Offset: 1

Views

Author

Labos Elemer, May 27 2003

Keywords

Crossrefs

Cf. A000040, A000720, A057855, A084295, A084297.

Programs

  • Mathematica
    Do[s=PrimePi[n*Prime[n]]/n; If[IntegerQ[s], Print[s]], {n, 1, 100000}]

Formula

a(n) = A000720(A084295(n)*A084297(n))/A084295(n).

Extensions

a(9)-a(12) from Giovanni Resta, Sep 02 2019
a(13) from Chai Wah Wu, May 14 2020

A084294 Number of primes in the interval [prime(n),n+prime(n)].

Original entry on oeis.org

2, 2, 2, 2, 2, 3, 3, 2, 3, 3, 3, 4, 4, 3, 4, 4, 5, 5, 5, 5, 4, 5, 5, 7, 6, 6, 5, 5, 5, 5, 7, 7, 7, 7, 8, 7, 8, 9, 8, 8, 7, 7, 9, 8, 9, 8, 9, 11, 10, 10, 11, 10, 10, 9, 10, 11, 10, 9, 9, 9, 8, 10, 11, 11, 10, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 14, 15, 14, 13
Offset: 1

Views

Author

Labos Elemer, May 27 2003

Keywords

Crossrefs

Cf. A000040, A000720, A061067, A061068, A084295.

Programs

  • Mathematica
    t[x_] := Table[w, {w, Prime[x], x+Prime[x]}] Table[Count[PrimeQ[t[n]], True], {n, 1, 128}] (* or *) Table[PrimePi[n+Prime[n]]-n+1, {n, 1, 25}];
  • PARI
    a(n) = primepi(n+prime(n)) - n + 1; \\ Michel Marcus, Aug 28 2019

Formula

a(n) = Pi(n+prime(n)) - n + 1 = A000720(n+A000040(n)) - n + 1. [corrected by Michel Marcus, Aug 28 2019]
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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