|
%I #16 Jan 12 2021 15:34:06
%S 1,1,2,2,8,36,288,1920,2880,120960,362880,6386688,34836480,217728000,
%T 3881779200,275904921600,1785411403776,28217548800000,608662978560000,
%U 3492203839488000,964122158039040000,2224367550332928000
%N a(n) = product of the remainders when the n-th prime is divided by primes up to the (n-1)-st prime.
%H Robert Israel, <a href="/A102647/b102647.txt">Table of n, a(n) for n = 1..413</a>
%e 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.
%p f:= proc(n) local p,i;
%p p:= ithprime(n);
%p mul(p mod ithprime(i),i=1..n-1)
%p end proc:
%p map(f, [$1..25]); # _Robert Israel_, Jan 12 2021
%t f[n_] := Times @@ Mod[ Prime[n], Table[ Prime[i], {i, n - 1}]]; Table[ f[n], {n, 22}] (* _Robert G. Wilson v_, Feb 04 2005 *)
%t Join[{0},Table[Times@@Mod[Prime[n],Prime[Range[n-1]]],{n,2,30}]] (* _Harvey P. Dale_, May 16 2019 *)
%o (PARI) a(n) = my(pr = 1, pn = prime(n)); forprime (q=1, precprime(pn-1), pr *= (pn % q)); pr; \\ _Michel Marcus_, Jan 12 2021
%Y Cf. A033955, A062347.
%K nonn
%O 1,3
%A Hans Boelens (h.p.m.boelens(AT)pl.hanze.nl), Feb 02 2005
%E More terms from _Robert G. Wilson v_, Feb 04 2005
%E a(1) (an empty product, therefore 1 by standard convention) corrected by _N. J. A. Sloane_, Jan 11 2021
|
