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Search: id:A152859
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| A152859 |
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Tower of prime powers: a(n)=prime(n)^a(n-1), a(0)=0. |
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+0
2
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| 0, 1, 3, 125, 43376549480979932825373547572631882516978329946204051017448930177445694327209941\ 68089672192211758909320807
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Originally called "Exprimorial numbers (exponential prime factorials)", the strict analogue would be "exponential primorial". [Editor's Note]
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LINKS
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Wikipedia, Factorial
J. Sondow, "Exponential Factorial."
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FORMULA
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a(n) = 0 if n = 0; a(n) = prime(n) ^ a(n - 1), n > = 1.
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EXAMPLE
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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
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PROGRAM
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(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]
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CROSSREFS
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Cf. A002110, A049384
Sequence in context: A085531 A130614 A114877 this_sequence A157547 A157562 A157592
Adjacent sequences: A152856 A152857 A152858 this_sequence A152860 A152861 A152862
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KEYWORD
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nonn
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AUTHOR
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ShaoJun Ying (dolphinysj(AT)gmail.com), Dec 14 2008
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EXTENSIONS
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Edited by M. F. Hasler (MHasler(AT)univ-ag.fr), Nov 01 2009
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