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.

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A195008 Numbers k such that there are no primes between k*sqrt(k-1) and (k+1)*sqrt(k).

Original entry on oeis.org

1, 24, 36, 47, 93, 105, 109, 117, 122, 207, 627, 996
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Sep 07 2011

Keywords

Comments

Numbers k such that there are only nonprimes between k*sqrt(k-1) and (k+1)*sqrt(k).
No more terms up to 100000. - Franklin T. Adams-Watters, Sep 08 2011
No more terms up to 364821. - J.W.L. (Jan) Eerland, Jan 21 2025

Examples

			a(1)=1 because 1*sqrt(1-1)=0<(nonprime 1)<(1+1)*sqrt(1)=2,
a(2)=24 because 24*sqrt(24-1)<(nonprimes 116,117,118,119,120,121,122)<(24+1)*sqrt(24).

Crossrefs

Cf. A195007.

Programs

  • Mathematica
    Join[{1},Select[Range[1000],PrimePi[# Sqrt[#-1]]==PrimePi[(#+1)Sqrt[#]]&]] (* Harvey P. Dale, Jun 01 2018 *)
  • PARI
    isa(n)=if(n<=1,n==1,primepi(floor(n*sqrt(n-1)))==primepi(floor((n+1)*sqrt(n))))

Extensions

a(11) and a(12) from Franklin T. Adams-Watters, Sep 08 2011
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