A079276 Multiplicative inverse in the finite field F(prime(n)) of the product of the first n-1 primes modulo prime(n).
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, 11, 30, 27, 49, 113, 63, 79, 25, 81, 143, 80, 121, 53, 142, 81, 52, 81, 150, 136, 40, 176, 114, 167, 138, 84, 46, 239, 213, 137, 4, 122, 136, 255, 141, 273, 30, 22, 25, 179, 9, 43, 12
Offset: 1
Keywords
Examples
a(6)=3 because 2*3*5*7*11 = 2310, 2310 == 9 (mod 13) and 9*(9^(-1)) == 9*3 == 1 (mod 13).
Links
- Eric Weisstein's World of Mathematics, Primorial
Programs
-
Maple
a := n -> (1/mul(ithprime(j), j=1..n-1)) mod ithprime(n); seq(a(n), n=1..68); # Peter Luschny, Apr 13 2014
-
Mathematica
a[n_] := Module[{i}, Return[PowerMod[Product[Prime[i], {i, 1, n - 1}], -1, Prime[n]]]; ];
Formula
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)).
Comments