A140319 Exponential primorial: a(n)=prime(n)^a(n-1), a(0)=1, where prime(n)=A000040(n).

1, 2, 9, 1953125

Offset: 0

Author

Paolo P. Lava and Giorgio Balzarotti, May 26 2008

Keywords

• easy
• nonn

Comments

The next term is too large to include.

Examples

			a(1) = prime(1)^a(0) = 2^1 = 2.
a(2) = 3^2 = 9.
a(3) = 5^9 = 1953125.
a(4) = 7^1953125 has 1650583 digits, starting with 12864794... and ending in ...31920807. - _M. F. Hasler_, Nov 03 2009
		

Links

• Jonathan Sondow, Exponential Factorial, Eric Weisstein's World of Mathematics.

Crossrefs

Cf. A002110, A049384, A139802, A167155.

Cf. A152859 (alternate definition: start with a(0)=0), A167155.

Programs

Maple

P:=proc(n) local a,i; a:=2; print(a); for i from 2 by 1 to n do a:=ithprime(i)^a; print(a); od; end: P(5);

Mathematica

a[0]=1;a[n_]:=Prime[n]^a[n-1];Array[a,4,0] (* James C. McMahon, Jul 08 2025 *)

PARI

A140319(n)=if(n,prime(n)^A140319(n-1),1) \\ M. F. Hasler, Nov 03 2009

Formula

Sum_{n>=0} 1/a(n) = A167155. - Amiram Eldar, Nov 15 2020

Extensions

Corrected offset/definition, and initial a(0)=1 from M. F. Hasler, Nov 03 2009