A245516 The smallest odd number k such that k^n-2 is a prime number.

5, 3, 9, 3, 3, 3, 7, 7, 3, 21, 9, 7, 19, 5, 7, 39, 15, 61, 15, 19, 21, 3, 19, 17, 21, 5, 21, 7, 85, 17, 7, 21, 511, 27, 27, 59, 3, 19, 91, 45, 3, 29, 321, 65, 9, 379, 69, 125, 49, 5, 9, 45, 289, 341, 61, 89, 171, 171, 139, 21, 139, 75, 25, 49, 15, 51, 57, 175

Offset: 1

Author

Lei Zhou, Jul 24 2014

Keywords

• nonn

Examples

			n=1, 3-2=1 is not prime, 5-2=3 is a prime number.  So a(1) = 5.
n=2, 3^2-2=7 is a prime number.  So a(2) = 3.
n=10, for k=3, 5, ..., 19, k^10-2 are all composite.  21^10-2 = 16679880978199 is a prime number.  So a(10) = 21.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A095303.

Programs

Maple

A245516 := proc(n)
    for k from 1 by 2 do
        if isprime(k^n-2) then
            return k;
        end if;
    end do:
end proc:
seq(A245516(n),n=1..60) ;

Mathematica

Table[n = 1;
While[n = n + 2; cp = n^i - 2; ! PrimeQ[cp]]; n, {i, 1, 68}]