A240234 Least number k such that k*n^k + 1 is prime, or 0 if no such number exists.

1, 1, 2, 1, 1242, 1, 34, 5, 2, 1, 10, 1

Offset: 1

Author

Derek Orr, Apr 02 2014

Keywords

• nonn
• hard
• more

Comments

a(n) = 1 if and only if n + 1 is prime.

Next term a(13), if it exists, is greater than 1000000. Other unknown terms are at index: 25, 29, 41, 47, 49, 53, 55, 69, 73, 79. (See links). - Jeppe Stig Nielsen, Aug 08 2014

Examples

			1*3^1 + 1 = 4 is not prime. 2*3^2 + 1 = 19 is prime. Thus, a(3) = 2.
		

Links

• Guenter Loeh, Generalized Cullen primes n b^n + 1
• Jeppe Stig Nielsen, Table of a(n) for n = 1..100, with unknown entries denoted by question marks

Crossrefs

Cf. A089001, A116954.

Programs

PARI

a(n) = for(k=1,4000,if(ispseudoprime(k*n^k+1),return(k)))
n=1;while(n<100,print1(a(n),", ");n++)