login
A090872
a(n) is the smallest number m greater than 1 such that m^(2^k)+1 for k=0,1,...,n are primes.
10
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
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
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
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