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A080208 a(n) is the least k such that the generalized Fermat number (k+1)^(2^n) + k^(2^n) is prime. 5
1, 1, 1, 1, 1, 8, 95, 31, 85, 59, 1078, 754, 311, 3508, 1828, 49957, 22844 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,6
COMMENTS
The first five terms correspond to the five known Fermat primes. The sequence A078902 lists some of the generalized Fermat primes. Bjorn and Riesel examined generalized Fermat numbers for k <= 11 and n <= 999. The sequence A080134 lists the conjectured number of primes for each k.
For n >= 10, a(n) yields a probable prime. a(13) was found by Henri Lifchitz. It is known that a(14) > 1000.
LINKS
Anders Björn and Hans Riesel, Factors of generalized Fermat numbers, Math. Comp. 67 (1998), no. 221, pp. 441-446.
Eric Weisstein's World of Mathematics, Generalized Fermat Number
FORMULA
a(n) = A253633(n) - 1.
EXAMPLE
a(5) = 8 because (k+1)^32 + k^32 is prime for k = 8 and composite for k < 8.
CROSSREFS
Sequence in context: A010565 A299002 A299669 * A297857 A298092 A298054
KEYWORD
hard,more,nonn
AUTHOR
T. D. Noe, Feb 10 2003
EXTENSIONS
a(14)-a(15) from Jeppe Stig Nielsen, Nov 27 2020
a(16) by Kellen Shenton communicated by Jeppe Stig Nielsen, May 19 2023
STATUS
approved

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Last modified June 18 04:26 EDT 2024. Contains 373468 sequences. (Running on oeis4.)