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URL: https://oeis.org/A102647

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A102647
a(n) = product of the remainders when the n-th prime is divided by primes up to the (n-1)-st prime.
9
1, 1, 2, 2, 8, 36, 288, 1920, 2880, 120960, 362880, 6386688, 34836480, 217728000, 3881779200, 275904921600, 1785411403776, 28217548800000, 608662978560000, 3492203839488000, 964122158039040000, 2224367550332928000, 1314079960596480000000, 3758268687305932800000
OFFSET
1,3
LINKS
EXAMPLE
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.
MAPLE
f:= proc(n) local p, i;
p:= ithprime(n);
mul(p mod ithprime(i), i=1..n-1)
end proc:
map(f, [$1..25]); # Robert Israel, Jan 12 2021
MATHEMATICA
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 *)
PROG
(PARI) a(n) = my(pr = 1, pn = prime(n)); forprime (q=1, precprime(pn-1), pr *= (pn % q)); pr; \\ Michel Marcus, Jan 12 2021
CROSSREFS
Sequence in context: A121197 A219348 A009543 * A318869 A060224 A232980
KEYWORD
nonn
AUTHOR
Hans Boelens (h.p.m.boelens(AT)pl.hanze.nl), Feb 02 2005
EXTENSIONS
More terms from Robert G. Wilson v, Feb 04 2005
a(1) (an empty product, therefore 1 by standard convention) corrected by N. J. A. Sloane, Jan 11 2021
STATUS
approved