cp's OEIS Frontend

A079276 Multiplicative inverse in the finite field F(prime(n)) of the product of the first n-1 primes modulo prime(n).

%I A079276 #15 Feb 16 2025 08:32:48
%S A079276 1,2,1,4,1,3,15,18,20,12,18,27,7,5,43,2,4,10,38,3,60,20,53,62,52,83,
%T A079276 11,30,27,49,113,63,79,25,81,143,80,121,53,142,81,52,81,150,136,40,
%U A079276 176,114,167,138,84,46,239,213,137,4,122,136,255,141,273,30,22,25,179,9,43,12
%N A079276 Multiplicative inverse in the finite field F(prime(n)) of the product of the first n-1 primes modulo prime(n).
%C A079276 a(n)=1 if and only if n-1 is in A341805. - _Jeppe Stig Nielsen_, Feb 20 2021
%H A079276 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Primorial.html">Primorial</a>
%F A079276 a(1) = 1; for n>1, a(n) = ( prime(n-1)# (mod prime(n)) )^(-1), where prime(i) is the i-th prime number, prime(i)# is the product of first i primes, x^(-1) is the multiplicative inverse in the finite field F(prime(n)).
%e A079276 a(6)=3 because 2*3*5*7*11 = 2310, 2310 == 9 (mod 13) and 9*(9^(-1)) == 9*3 == 1 (mod 13).
%p A079276 a := n -> (1/mul(ithprime(j), j=1..n-1)) mod ithprime(n);
%p A079276 seq(a(n), n=1..68); # _Peter Luschny_, Apr 13 2014
%t A079276 a[n_] := Module[{i}, Return[PowerMod[Product[Prime[i], {i, 1, n - 1}], -1, Prime[n]]]; ];
%Y A079276 Cf. A062347, A002110, A000040, A240673, A341805.
%K A079276 nonn
%O A079276 1,2
%A A079276 Valentin F. Schmid (v_schmid(AT)hotmail.com), Feb 07 2003