A007516 (2^2^...^2) (n times) + 1.

1, 3, 5, 17, 65537

Offset: 0

Author

N. J. A. Sloane and Robert G. Wilson v

Keywords

• nonn

Comments

a(0) could equally well be taken to be 2 rather than 1, which gives A004249. - N. J. A. Sloane, Sep 14 2009

The next term already has 19729 digits and is too large to include. - Stefan Steinerberger, Apr 14 2006

References

• P. Ribenboim, The Book of Prime Number Records. Springer-Verlag, NY, 2nd ed., 1989, p. 73.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Crossrefs

Cf. A004249 (another version).

Programs

Mathematica

a[1] := 1; a[2] := 3; a[n_] := 2^(a[n - 1] - 1) + 1; Table[a[n], {n, 1, 5}] (* Stefan Steinerberger, Apr 14 2006 *)

Formula

a(1) = 1, a(2) = 3, a(n+1) = 2^(a(n)-1) + 1. - Stefan Steinerberger, Apr 14 2006