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Search: id:A049782
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| A049782 |
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a(n)=(0! + 1! + ... + (n-1)!) mod n. |
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+0
5
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| 0, 0, 1, 2, 4, 4, 6, 2, 1, 4, 1, 10, 10, 6, 4, 10, 13, 10, 9, 14, 13, 12, 21, 10, 14, 10, 10, 6, 17, 4, 2, 26, 1, 30, 34, 10, 5, 28, 10, 34, 4, 34, 16, 34, 19, 44, 18, 10, 48, 14, 13, 10, 13, 10, 34, 34, 28, 46, 28, 34, 22, 2, 55, 26, 49, 34, 65, 30, 67, 34, 68, 10, 55, 42, 64, 66, 34
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Kurepa's conjecture is that (!n,n!)=2, n>1. It is easy to prove that this is equivalent to showing that (p,!p)=1 for all odd primes p. In Guy, 2nd edition, it is stated that Mijajlovic has tested up to p=10^6. Subsequently Gallot tested up to 2^26. I have continued up to just above p=2^27, in fact to p<144000000. There were no examples found where (p, !p)>1. - Paul Jobling, Dec 02 2004
According to Kellner, the conjecture has been proved by Barsky and Benzaghou. - T. D. Noe (noe(AT)sspectra.com), Dec 02 2004
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REFERENCES
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D. Barsky and B. Benzaghou, Nombres de Bell et somme de factorielles, Journal de Theorie des Nombres de Bordeaux, 16:1, No. 17, 2004.
R. K. Guy, Unsolved Problems in Number Theory, B44: is a(n)>0 for n>2?
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
Y. Gallot, More information
Bernd C. Kellner, Some remarks on Kurepa's left factorial (pdf)
S. A. Silver, C program to generate this sequence
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MATHEMATICA
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Table[ Mod[ Sum[ i!, {i, 0, n-1} ], n ], {n, 1, 120} ]
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CROSSREFS
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Sequence in context: A151969 A121528 A160904 this_sequence A091666 A084290 A062011
Adjacent sequences: A049779 A049780 A049781 this_sequence A049783 A049784 A049785
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
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More terms from Erich Friedman (erich.friedman(AT)stetson.edu), who observes that the first 500 terms are nonzero. Independently extended by Stephen A. Silver (maths(AT)argentum.freeserve.co.uk).
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