A245811 Number of primes of the form k^(n+1) - n^k for some k > 1.

1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 22 2014

Keywords

• nonn

Comments

The search radius for k is effectively limited to k<=n+1 because the subtracted term n^k has exponential growth and the added term k^(n+1) only polynomial growth as k increases. - R. J. Mathar, Sep 07 2014

Links

• Juri-Stepan Gerasimov, Table of n, a(n) for n = 1..78

Crossrefs

Cf. A245809.

Programs

Maple

A245811 := proc(n)
    local a,k,p ;
    a := 0 ;
    for k from 2 to n+1 do
        p := k^(n+1)-n^k ;
        if isprime(p) then
             a := a+1 ;
        end if;
    end do:
    a ;
end proc:
seq(A245811(n),n=1..120) ; # R. J. Mathar, Sep 07 2014

PARI

a(n) = if(n==1, return(1)); my(k=2, c=0, t); while((t=k^(n+1)-n^k)>0, k++; if(isprime(t), c++)); c
vector(80, n, a(n)) \\ Colin Barker, Aug 26 2014