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 1-2 of 2 results.

A195007 Number of primes in the range (n*sqrt(n-1), (n+1)*sqrt(n)].

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 3, 2, 0, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 0, 3, 2, 1, 2, 1, 3, 2, 1, 1, 3, 0, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 3, 1, 3, 1, 2, 2, 1, 2, 1, 1, 2, 3, 2, 2, 4, 1, 2, 2, 2, 3, 1, 2, 1, 2, 3, 2, 2, 1, 1
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Sep 07 2011

Keywords

Examples

			a(1)=1`because 1*sqrt(1-1)<(prime 2)<=(1+1)*sqrt(1),
a(2)=1 because 2*sqrt(2-1)<(prime 3)<=(2+1)*sqrt(2).

Crossrefs

Cf. A006005, A192454.

Programs

  • Mathematica
    Table[PrimePi[(n+1)*Sqrt[n]] - PrimePi[n*Sqrt[n-1]], {n, 100}] (* T. D. Noe, Sep 14 2011 *)

A195351 Numbers k such that there are no primes in the range [2^k-k, 2^k+k].

Original entry on oeis.org

0, 25, 27, 45, 49, 97, 99, 113, 139, 176, 186, 208, 216, 227, 232, 259, 298, 309, 332, 358, 362, 364, 387, 490, 631, 659, 662, 676, 698, 705, 718, 726, 737, 747, 781, 849, 860, 862, 901, 913, 918, 936, 958, 965, 966, 992, 998
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Sep 16 2011

Keywords

Comments

If a(n) is prime then it is not in A000043. - Alonso del Arte, Oct 07 2011

Crossrefs

Cf. A192454.

Programs

  • Mathematica
    Select[Range[0, 49], PrimePi[2^# - # - 1] == PrimePi[2^# + #] &] (* Alonso del Arte, Oct 07 2011 *)

Formula

A192454(a(n))=0.
Showing 1-2 of 2 results.

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