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A079276 Multiplicative inverse in the finite field F(prime(n)) of the product of the first n-1 primes modulo prime(n). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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(p(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.

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

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Last modified September 21 19:39 EDT 2019. Contains 327279 sequences. (Running on oeis4.)