A152859 Tower of prime powers: a(n)=prime(n)^a(n-1), a(0)=0.

0, 1, 3, 125, 4337654948097993282537354757263188251697832994620405101744893017744569432720994168089672192211758909320807

Offset: 0

Author

ShaoJun Ying (dolphinysj(AT)gmail.com), Dec 14 2008

Keywords

• nonn

Comments

Originally called "Exprimorial numbers (exponential prime factorials)", the strict analog would be "exponential primorial". [Editor's Note]

Examples

			a(4) = 7 ^ a(3) = 7 ^ 125.
a(5) = 11 ^ a(4) has approximately 4.5 * 10^105 digits, starting with 335856... and ending in ...815171.
		

Links

• J. Sondow, Exponential Factorial
• Wikipedia, Factorial

Crossrefs

Cf. A002110, A049384.

Cf. A140319 (alternate definition: start with a(0)=1). - Paolo P. Lava, Jul 31 2018

Programs

C

unsigned long Exprimorial(unsigned int n) {
if (n == 0) return 0;
return pow(prime(n),Exprimorial(n - 1));
}

PARI

vector(4,i,t=if(i==1,1,prime(i)^t)) /* indices are shifted by 1 */ \\ M. F. Hasler, Nov 01 2009

Formula

a(n) = 0 if n = 0; a(n) = prime(n) ^ a(n - 1), n >= 1.

Extensions

Edited by M. F. Hasler, Nov 01 2009