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 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 5 16:50 EDT 2023. Contains 363137 sequences. (Running on oeis4.)