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A102647
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a(n) = product of the remainders when the n-th prime is divided by primes up to the (n-1)-st prime.
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8
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1, 1, 2, 2, 8, 36, 288, 1920, 2880, 120960, 362880, 6386688, 34836480, 217728000, 3881779200, 275904921600, 1785411403776, 28217548800000, 608662978560000, 3492203839488000, 964122158039040000, 2224367550332928000
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OFFSET
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1,3
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LINKS
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EXAMPLE
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Prime(6) = 13, 13 mod 2 = 1, 13 mod 3 = 1, 13 mod 5 = 3, 13 mod 7 = 6, 13 mod 11 = 2 so a(6) = 1*1*3*6*2 = 36.
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MAPLE
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f:= proc(n) local p, i;
p:= ithprime(n);
mul(p mod ithprime(i), i=1..n-1)
end proc:
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MATHEMATICA
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f[n_] := Times @@ Mod[ Prime[n], Table[ Prime[i], {i, n - 1}]]; Table[ f[n], {n, 22}] (* Robert G. Wilson v, Feb 04 2005 *)
Join[{0}, Table[Times@@Mod[Prime[n], Prime[Range[n-1]]], {n, 2, 30}]] (* Harvey P. Dale, May 16 2019 *)
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PROG
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(PARI) a(n) = my(pr = 1, pn = prime(n)); forprime (q=1, precprime(pn-1), pr *= (pn % q)); pr; \\ Michel Marcus, Jan 12 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Hans Boelens (h.p.m.boelens(AT)pl.hanze.nl), Feb 02 2005
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EXTENSIONS
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a(1) (an empty product, therefore 1 by standard convention) corrected by N. J. A. Sloane, Jan 11 2021
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STATUS
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approved
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