A004249 a(n) = (2^2^...^2) (with n 2's) + 1.

2, 3, 5, 17, 65537

Offset: 0

Author

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

Keywords

• nonn

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. Springer-Verlag, NY, 2nd ed., 1989, p. 73.

Links

• Y. Bugeaud and M. Queffélec, On Rational Approximation of the Binary Thue-Morse-Mahler Number, Journal of Integer Sequences, 16 (2013), #13.2.3.
• Wilfrid Keller, Prime factors k.2^n + 1 of Fermat numbers F_m

Crossrefs

Cf. Fermat numbers 2^2^n + 1 = A000215. A007516 is another version.

Formula

a(0) = 2, a(n) = 2^a(n-1)/2 + 1 for n >= 1.

a(n) = A014221(n) + 1. - Leroy Quet, Jun 10 2009, updated by Jeppe Stig Nielsen, Jun 15 2022