A102647 a(n) = product of the remainders when the n-th prime is divided by primes up to the (n-1)-st prime.

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

Author

Hans Boelens (h.p.m.boelens(AT)pl.hanze.nl), Feb 02 2005

Keywords

• nonn

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..413

Crossrefs

Cf. A033955, A062347.

Programs

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 *)

PARI

a(n) = my(pr = 1, pn = prime(n)); forprime (q=1, precprime(pn-1), pr *= (pn % q)); pr; \\ Michel Marcus, Jan 12 2021

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