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Search: id:A073828
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| A073828 |
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Primes of the form 1 + 0!*1!*2!*...*n! (subsequence of A019515). |
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+0
3
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| 2, 2, 3, 13, 125411328001, 69113789582492712943486800506462734562847413501952000000000000001
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(4) = 125411328001 and the 65-digit a(5) have been certified prime with Primo. Any additional terms are too big to include here. a(3) = 13 and a(4) have twin primes, 11 and 125411327999 (also certified prime with Primo). No other primes of the form 0!*1!*2!*...*n! - 1 exist for n < 108.
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REFERENCES
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Ryser, H. J. Combinatorial Mathematics. Buffalo, NY: Math. Assoc. Amer., p. 53, 1963.
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LINKS
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M. Fleuren, Smarandache Factorial Products.
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FORMULA
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a(k) = 1 + 0!*1!*2!*...*A073827(k)!.
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EXAMPLE
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a(0) = 1 + 0! (0=A073827(0)) = 1 + 1 = 2. a(1) = 1 + 0!*1! (1=A073827(1)) = 1 + 1*1 = 2. a(4) = 1 + 0!*1!*2!*3!*4!*5!*6!*7! (7=A073827(4)) = 1 + 1*1*2*6*24*120*720*5040 = 125411328001
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PROGRAM
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(PARI) pr=1; for(n=0, 115, pr=pr*n!; if(isprime(pr+1), print1(pr+1, ", ")))
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CROSSREFS
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Cf. A073827 (corresponding n), A000178 (superfactorials), A019515 (supersequence: superfactorials + 1), A000142 (factorials).
Sequence in context: A139521 A019515 A094352 this_sequence A153938 A060790 A109843
Adjacent sequences: A073825 A073826 A073827 this_sequence A073829 A073830 A073831
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KEYWORD
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nonn
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AUTHOR
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Rick L. Shepherd (rshepherd2(AT)hotmail.com), Aug 16 2002
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