A090872 a(n) is the smallest number m greater than 1 such that m^(2^k)+1 for k=0,1,...,n are primes.

2, 2, 2, 2, 2, 7072833120, 2072005925466, 240164550712338756

Offset: 0

Author

Farideh Firoozbakht, Jan 31 2004

Keywords

• nonn
• more

Comments

The first five terms of this sequence correspond to Fermat primes.

Note that 7072833120 is not the smallest base to give at least six possibly nonconsecutive k values. For example, 292582836^(2^k) + 1 is prime for k = 0,1,2,3,4,7. - Jeppe Stig Nielsen, Sep 18 2022

Examples

			a(5)=7072833120 because 7072833120^2^k+1 for k=0,1,2,3,4,5 are primes.
		

Links

• PrimeGrid, Generalized Fermat Progression Search
• Carlos Rivera, Puzzle 137. Product of primes + 1, a square, The Prime Puzzles and Problems Connection.
• Carlos Rivera, Prime Puzzle 399. Some more terms, The Prime Puzzles and Problems Connection.

Crossrefs

Cf. A019434, A000215.

Cf. A090873, A090874, A090875.

All solutions for fixed n: A006093 (n=0), A070689 (n=1), A070325 (n=2), A070655 (n=3), A070694 (n=4), A235390 (n=5), A335805 (n=6), A337364 (n=7).

Extensions

a(6) from Jens Kruse Andersen, May 06 2007

a(7) from Kellen Shenton, Aug 13 2020