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

0,1

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

Links

Table of n, a(n) for n=0..7.

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.

Example

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

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).

Sequence in context: A067089 A339027 A343121 * A283472 A225538 A212355

Adjacent sequences: A090869 A090870 A090871 * A090873 A090874 A090875

Keyword

nonn,more

Author

Farideh Firoozbakht, Jan 31 2004

Extensions

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

a(7) from Kellen Shenton, Aug 13 2020

Status

approved