A242803 Least number k such that (k^k+n)/(k+n) is prime or 0 if no such number exists.

3, 4, 3, 0, 4, 491, 9, 5, 3, 4, 0, 16, 0, 7, 5, 0, 4, 20, 5, 85, 3, 64, 25, 15, 625, 0, 10, 0, 7, 19, 7, 9, 0, 15, 5, 0, 0, 4, 16, 25, 0, 0, 17, 11, 0, 16, 5, 0, 0, 7, 31, 0, 31, 100, 5, 0, 0, 0, 4, 0, 0, 0, 9, 0, 13, 0, 0, 0, 7, 0, 10, 0, 5, 0, 0, 0, 0, 0, 51, 0, 0, 0, 0, 136

Offset

1,1

Comments

a(n) = 0 is confirmed only for k <= 5000, they are not definite.

Links

Table of n, a(n) for n=1..84.

Example

(1^1+3)/(1+3) = 1 is not prime. (2^2+3)/(2+3) = 7/5 is not prime. (3^3+3)/(3+3) = 30/6 = 5 is prime. Thus a(3)= 3.

Prog

(PARI) a(n)=for(k=1, 1500, s=(k^k+n)/(k+n); if(floor(s)==s, if(ispseudoprime(s), return(k))));
n=1; while(n<100, print(a(n)); n+=1)

Crossrefs

Sequence in context: A244042 A318840 A318830 * A064460 A108481 A367076

Adjacent sequences: A242800 A242801 A242802 * A242804 A242805 A242806

Keyword

nonn,more,hard

Author

Derek Orr, May 23 2014

Status

approved