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A228037
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Odd-indexed terms of Agoh's congruence A046094: a(n) is conjectured to be 1 iff 2n+1 is prime.
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4
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0, 1, 1, 1, 3, 1, 1, 5, 1, 1, 7, 1, 5, 9, 1, 1, 11, 0, 1, 13, 1, 1, 24, 1, 7, 17, 1, 0, 19, 1, 1, 21, 13, 1, 23, 1, 1, 25, 0, 1, 27, 1, 17, 29, 1, 13, 31, 0, 1, 33, 1, 1, 56, 1, 1, 37, 1, 0, 39, 0, 11, 41, 25, 1, 43, 1, 19, 45, 1, 1, 47, 0, 29, 49, 1, 1, 51, 0, 1, 53, 0, 1, 88, 1, 13, 57, 1, 25, 59, 1, 1, 61, 37, 0, 63, 1, 1, 65, 1
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OFFSET
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0,5
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COMMENTS
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Except for A046094(2) = 1, the even-indexed terms of A046094 are all zero since Bernoulli(2n+1) = 0 for n > 0.
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LINKS
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FORMULA
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a(n) = - (2n+1)*Bernoulli(2n) mod 2n+1.
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EXAMPLE
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-(2*1+1)*Bernoulli(2*1) = -3*(1/6) = -1/2 == -2 == 1 mod 3, so a(1) = 1.
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MAPLE
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a:= n-> -(2*n+1)*bernoulli(2*n) mod (2*n+1):
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MATHEMATICA
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a[ n_ ] := Mod[ Numerator[ -(2 n + 1)* BernoulliB[ 2 n]] * PowerMod[ Denominator[(2 n + 1)* BernoulliB[ 2 n]], -1, 2 n + 1], 2 n + 1]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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