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

1,2

Comments

a(n)=1 if and only if n-1 is in A341805. - Jeppe Stig Nielsen, Feb 20 2021

Links

Table of n, a(n) for n=1..68.

Eric Weisstein's World of Mathematics, Primorial

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)).

Example

a(6)=3 because 2*3*5*7*11 = 2310, 2310 == 9 (mod 13) and 9*(9^(-1)) == 9*3 == 1 (mod 13).

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]]]; ];

Crossrefs

Cf. A062347, A002110, A000040, A240673, A341805.

Sequence in context: A049776 A286235 A180339 * A210445 A126210 A040005

Adjacent sequences: A079273 A079274 A079275 * A079277 A079278 A079279

Keyword

nonn

Author

Valentin F. Schmid (v_schmid(AT)hotmail.com), Feb 07 2003

Status

approved