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

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

Offset

1,2

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

Links

Table of n, a(n) for n=1..12.

Example

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).

Mathematica

Join[{1}, Select[Range[1000], PrimePi[# Sqrt[#-1]]==PrimePi[(#+1)Sqrt[#]]&]] (* Harvey P. Dale, Jun 01 2018 *)

Prog

(PARI) isa(n)=if(n<=1, n==1, primepi(floor(n*sqrt(n-1)))==primepi(floor((n+1)*sqrt(n))))

Crossrefs

Cf. A195007.

Sequence in context: A307682 A290016 A330880 * A054775 A273088 A334674

Adjacent sequences: A195005 A195006 A195007 * A195009 A195010 A195011

Keyword

nonn,more,hard

Author

Juri-Stepan Gerasimov, Sep 07 2011

Extensions

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

Status

approved