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



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.


Table of n, a(n) for n=0..15.

T. D. Noe, Table of generalized Fermat primes of the form (k+1)^2^m + k^2^m

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


a(n) = A253633(n) - 1.


a(5) = 8 because (k+1)^32 + k^32 is prime for k = 8 and composite for k < 8.


Cf. A019434, A078902, A080134, A153504, A152913, A194185, A253633.

Sequence in context: A010565 A299002 A299669 * A297857 A298092 A298054

Adjacent sequences: A080205 A080206 A080207 * A080209 A080210 A080211




T. D. Noe, Feb 10 2003


a(14)-a(15) from Jeppe Stig Nielsen, Nov 27 2020



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Last modified December 4 23:46 EST 2022. Contains 358572 sequences. (Running on oeis4.)