A352736 a(n) is the smallest b >= 2 such that 1 + Sum_{k=0..n} b^(2^k) is prime, or 1 if no such b exists.

2, 2, 2, 1, 6, 3, 448, 107, 104, 1, 4556, 1, 24124, 121209, 368, 177817, 48330, 1

Offset: 0

Author

Kellen Shenton, Mar 30 2022

Keywords

• nonn
• hard
• more

Comments

Polynomial factorizations exist for n=3,9,11,17,27 and may exist for other n > 27.

For those n for which a proven factorization exists, b=1 results in a prime of the form n+2.

Examples

			a(6)=448 because 448 is the smallest number b such that 1 + Sum_{k=0..6} b^(2^k) is prime.
		

Extensions

a(16)-a(17) from Kellen Shenton, May 08 2022