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A046094
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Agoh's congruence; a(n) is conjectured to be 1 iff n is prime.
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4
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0, 1, 1, 0, 1, 0, 1, 0, 3, 0, 1, 0, 1, 0, 5, 0, 1, 0, 1, 0, 7, 0, 1, 0, 5, 0, 9, 0, 1, 0, 1, 0, 11, 0, 0, 0, 1, 0, 13, 0, 1, 0, 1, 0, 24, 0, 1, 0, 7, 0, 17, 0, 1, 0, 0, 0, 19, 0, 1, 0, 1, 0, 21, 0, 13, 0, 1, 0, 23, 0, 1, 0, 1, 0, 25, 0, 0, 0, 1, 0, 27, 0, 1, 0, 17, 0, 29, 0, 1, 0, 13, 0, 31, 0, 0, 0, 1, 0
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OFFSET
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1,9
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LINKS
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D. Borwein, J. M. Borwein, P. B. Borwein and R. Girgensohn, Giuga's conjecture on primality, The American Mathematical Monthly, Vol. 103, No. 1 (1996), 40-50.
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FORMULA
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a(n) = - n*Bernoulli(n-1) mod n.
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EXAMPLE
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- 21 * Bernoulli(20) = 21 * 174611 / 330 = 1222277 / 110 and 1 / 110 == 17 mod 21, so a(21) = 1222277 * 17 mod 21 = 7. - Jonathan Sondow, Aug 13 2013
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MATHEMATICA
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a[ n_ ] := Mod[ Numerator[ -n* BernoulliB[ n-1 ]]*PowerMod[ Denominator[ n*BernoulliB[ n-1 ] ], -1, n ], n ] (* Jonathan Sondow, Aug 13 2013 *)
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PROG
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(PARI) a(n) = -n*bernfrac(n-1) % n; \\ Michel Marcus, Aug 08 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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a(21), a(51), a(57), a(65), a(81) corrected by Jonathan Sondow, Aug 13 2013
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STATUS
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approved
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