A060377 Pepin's test numbers.

3, 9, 6561, 11790184577738583171520872861412518665678211592275841109096961

Offset: 0

Author

Jason Earls, Apr 02 2001

Keywords

• nonn

Comments

Next two terms have 15635 and 1024610093 digits respectively. [Corrected by Michael S. Branicky and Sean A. Irvine, Nov 12 2022]

Examples

			a(1) = 3^((F(1)-1)/2) = 3^((5-1)/2) = 3^2 = 9.
		

Links

• C. K. Caldwell, Pepin's Test.

Crossrefs

Cf. A000215.

Programs

Mathematica

A000215[n_]:=2^(2^n)+1; a[n_]:=3^((A000215[n]-1)/2); Array[a,4,0] (* Stefano Spezia, Sep 14 2024 *)

Python

def a(n): return 3**(2**(2**n-1))
print([a(n) for n in range(4)]) # Michael S. Branicky, Nov 12 2022

Formula

a(n) = 3^((F(n)-1)/2) where F(n) is a Fermat number (A000215).

Extensions

Corrected offset, formula and example Harry J. Smith, Jul 04 2009