

A004249


a(n) = (2^2^...^2) (with n 2's) + 1.


8




OFFSET

0,1


COMMENTS

a(0) could equally well be taken to be 1 rather than 2, which gives A007516.  N. J. A. Sloane, Sep 14 2009
A subsequence of the Fermat numbers 2^2^n + 1 = A000215.
a(0) through a(4) are primes; a(5) = 2^65536 + 1 is divisible by 825753601.
a(5) = 20035299...19156737 has 19729 decimal digits.  Alois P. Heinz, Jun 15 2022
It is unknown if a(6) = A000215(65536) is composite.  Jeppe Stig Nielsen, Jun 15 2022


REFERENCES

P. Ribenboim, The Book of Prime Number Records. SpringerVerlag, NY, 2nd ed., 1989, p. 73.


LINKS

Table of n, a(n) for n=0..4.
Y. Bugeaud and M. QueffĂ©lec, On Rational Approximation of the Binary ThueMorseMahler Number, Journal of Integer Sequences, 16 (2013), #13.2.3.
Wilfrid Keller, Prime factors k.2^n + 1 of Fermat numbers F_m


FORMULA

a(0) = 2, a(n) = 2^a(n1)/2 + 1 for n >= 1.
a(n) = A014221(n) + 1.  Leroy Quet, Jun 10 2009, updated by Jeppe Stig Nielsen, Jun 15 2022


CROSSREFS

Cf. Fermat numbers 2^2^n + 1 = A000215. A007516 is another version.
Sequence in context: A127063 A127837 A253646 * A268210 A121510 A132346
Adjacent sequences: A004246 A004247 A004248 * A004250 A004251 A004252


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Robert G. Wilson v, David W. Wilson


STATUS

approved



