A226367 Multiplicative order of the (n+1)-st prime modulo the n-th prime.

1, 2, 4, 3, 10, 6, 8, 9, 11, 28, 6, 18, 20, 7, 23, 26, 58, 60, 33, 35, 36, 39, 82, 11, 24, 100, 51, 106, 18, 28, 7, 130, 68, 46, 148, 150, 156, 81, 83, 43, 178, 180, 95, 48, 196, 66, 14, 37, 226, 38, 232, 119, 30, 250, 256, 131, 268, 270, 46, 70, 141, 146, 51, 155, 78, 316, 165, 336, 346, 174, 32, 179, 366, 372, 189

Offset: 1

Author

Emmanuel Vantieghem, Jun 05 2013

Keywords

• nonn

Comments

a(n) is the smallest positive integer m with the property that p(n+1)^m == 1 (mod p(n)), where p(n) stands for the n-th prime; it is always a divisor of p(n)-1. For n < 10^8, a(n) is never equal to A226295(n).

Examples

			a(2) = 2 because 5^2 == 1 (mod 3) but 5^1 !== 1(mod 3).
a(6) = 6  because 17^6 == 1 (mod 13) but 17^u !== 1 (mod 13) for  u < 6.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A226295 (multiplicative order of p(n) mod p(n+1)).

Programs

Mathematica

Table[MultiplicativeOrder[Prime[n+1],Prime[n]],{n,1,75}]

PARI

vector(80, n, p = prime(n); znorder(Mod(nextprime(p+1), p))) \\ Michel Marcus, Feb 09 2015