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A002068
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Wilson remainders: a(n) = ((p-1)!+1)/p mod p, where p=prime(n).
(Formerly M3728 N1524)
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6
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1, 1, 0, 5, 1, 0, 5, 2, 8, 18, 19, 7, 16, 13, 6, 34, 27, 56, 12, 69, 11, 73, 20, 70, 70, 72, 57, 1, 30, 95, 71, 119, 56, 67, 94, 86, 151, 108, 21, 106, 48, 72, 159, 35, 147, 118, 173, 180, 113, 131, 169, 107, 196, 214, 177, 73, 121, 170, 25, 277, 164, 231, 271, 259, 288, 110
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| If this is zero, p is a Wilson prime (see A007540).
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REFERENCES
| R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see p. 29.
C.-E. Froberg, Investigation of the Wilson remainders in the interval 3<=p<=50,000, Arkiv f. Matematik, 4 (1961), 479-481.
K. Goldberg, A table of Wilson quotients and the third Wilson prime, J. London Math. Soc., 28 (1953), 252-256.
J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 244.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..2000
J. Sondow, Lerch Quotients, Lerch Primes, Fermat-Wilson Quotients, and the Wieferich-non-Wilson Primes 2, 3, 14771, in Proceedings of CANT 2011, arXiv:1110.3113
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FORMULA
| a(n) = A007619(n) mod A000040(n)
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MATHEMATICA
| Table[p=Prime[n]; Mod[((p-1)!+1)/p, p], {n, 100}] - T. D. Noe (noe(AT)sspectra.com), Mar 21 2006
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CROSSREFS
| Sequence in context: A102259 A021200 A019904 * A021666 A143148 A198541
Adjacent sequences: A002065 A002066 A002067 * A002069 A002070 A002071
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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