A118710 Smallest positive integer k such that k^k + F(n) is prime, where F(n) is the n-th Fibonacci number.

1, 1, 1, 2, 444

Offset: 1

Author

Ryan Propper, May 20 2006

Keywords

• hard
• more
• nonn

Comments

Next term is not known. Sequence continues: 1, 1, 1, 2, 444, ?, 2, 4, 3, 2, ?, ?, 6, ?, 1059, 2, 2, ?, ?, 14, 3, 66, 2, ?, 2, 46, 15, 8, 78, 273, 2, 2. All unknown terms are >= 2000. All known terms except a(15) = 1059 correspond to certified primes.

a(6) = A087037(8) > 30300.

Programs

Mathematica

Do[k = 1; While[ !PrimeQ[k^k + Fibonacci[n]], k++ ]; Print[k], {n, 32}]

Formula

a(n) = A087037(A000045(n)).