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

%I A152859 #18 Feb 16 2025 08:33:09
%S A152859 0,1,3,125,
%T A152859 4337654948097993282537354757263188251697832994620405101744893017744569432720994168089672192211758909320807
%N A152859 Tower of prime powers: a(n)=prime(n)^a(n-1), a(0)=0.
%C A152859 Originally called "Exprimorial numbers (exponential prime factorials)", the strict analog would be "exponential primorial". [Editor's Note]
%H A152859 J. Sondow, <a href="https://mathworld.wolfram.com/ExponentialFactorial.html">Exponential Factorial</a>
%H A152859 Wikipedia, <a href="http://en.wikipedia.org/wiki/Factorial">Factorial</a>
%F A152859 a(n) = 0 if n = 0; a(n) = prime(n) ^ a(n - 1), n >= 1.
%e A152859 a(4) = 7 ^ a(3) = 7 ^ 125.
%e A152859 a(5) = 11 ^ a(4) has approximately 4.5 * 10^105 digits, starting with 335856... and ending in ...815171.
%o A152859 (C) unsigned long Exprimorial(unsigned int n) {
%o A152859 if (n == 0) return 0;
%o A152859 return pow(prime(n),Exprimorial(n - 1));
%o A152859 }
%o A152859 (PARI) vector(4,i,t=if(i==1,1,prime(i)^t)) /* indices are shifted by 1 */ \\ _M. F. Hasler_, Nov 01 2009
%Y A152859 Cf. A002110, A049384.
%Y A152859 Cf. A140319 (alternate definition: start with a(0)=1). - _Paolo P. Lava_, Jul 31 2018
%K A152859 nonn
%O A152859 0,3
%A A152859 ShaoJun Ying (dolphinysj(AT)gmail.com), Dec 14 2008
%E A152859 Edited by _M. F. Hasler_, Nov 01 2009