A283419 a(n) is the multiplicative inverse of 3 modulo the n-th prime (or 0 if none exists).

1, 0, 2, 5, 4, 9, 6, 13, 8, 10, 21, 25, 14, 29, 16, 18, 20, 41, 45, 24, 49, 53, 28, 30, 65, 34, 69, 36, 73, 38, 85, 44, 46, 93, 50, 101, 105, 109, 56, 58, 60, 121, 64, 129, 66, 133, 141, 149, 76, 153, 78, 80, 161, 84, 86, 88, 90, 181, 185, 94, 189, 98, 205, 104, 209, 106, 221, 225

Offset

1,3

Links

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

Eric Weisstein's MathWorld, Modular Inverse

Formula

3 * a(n) == 1 (mod prime(n)).

a(n) = (p * (-1)^((r+1)/2))/3 mod p = q * (-1)^((r+1)/2) mod p where p = prime(n) = 3*q + r, with r = -1 or 1 and quotient q a positive integer. - Ian George Walker, Mar 24 2021

a(n) = ceiling(2p/3)/(p mod 3) where p is the n-th prime, a(2)=0. - Travis Scott, Feb 08 2023

Example

3*5 mod prime(4) = 15 mod 7 = 1, so a(4) = 5.

Maple

a:= n-> `if`(n=2, 0, (p-> ceil(2*p/3)/(p mod 3))(ithprime(n))):
seq(a(n), n=1..75);  # Alois P. Heinz, Feb 08 2023

Mathematica

a[n_] := ModularInverse[3, Prime[n]]; Table[a[n], {n, 3, 100}]
Table[If[Mod[Prime@n, 3]==0, 0, ModularInverse[3, Prime@n]], {n, 88}]

Prog

(PARI) a(n) = if (n==2, 0, lift(1/Mod(3, prime(n)))); \\ Michel Marcus, Mar 31 2021

Crossrefs

Cf. A006254 (modular inverses of 2 modulo the odd primes).

Sequence in context: A214533 A065221 A373053 * A114752 A204923 A123302

Adjacent sequences: A283416 A283417 A283418 * A283420 A283421 A283422

Keyword

nonn

Author

Jean-François Alcover, May 02 2017

Extensions

Name edited and a(1)-a(2) prepended by Travis Scott, Feb 08 2023

Status

approved