A226295 Multiplicative order of the n-th prime modulo the (n+1)th prime.

2, 4, 6, 10, 12, 4, 9, 22, 7, 10, 4, 5, 7, 46, 13, 29, 60, 66, 70, 18, 39, 82, 88, 16, 25, 102, 106, 36, 7, 63, 130, 136, 69, 148, 30, 156, 54, 166, 86, 89, 180, 190, 96, 49, 198, 7, 111, 226, 76, 58, 34, 24, 25, 256, 262, 67, 270, 276, 70, 47, 73, 153, 310

Offset

1,1

Comments

a(n) is the smallest positive integer m such that p(n)^m == 1 (mod p(n+1)), where p(n) stands for the n-th prime.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

K. Kashihara, Comments and Topics on Smarandache Notions and Problems, Erhus University Press, 1996, 50 pages. See page 44.

K. Kashihara, Comments and Topics on Smarandache Notions and Problems, Erhus University Press, 1996, 50 pages. [Cached copy] See page 44.

Example

a(n) = 2 because 2^2 == 1 (mod 3) but 2^1 !== 1 (mod 3); a(6) = 4 because 13^4 == 1 (mod 17) but 13^u !== 1 (mod 17) for u = 1, 2, 3.

Mathematica

Table[MultiplicativeOrder[Prime[n], Prime[n+1]], {n, 80}]

Prog

(PARI) a(n)=my(p=prime(n)); znorder(Mod(p, nextprime(p+1))) \\ Charles R Greathouse IV, Jun 04 2013
(Python)
from sympy import prime, n_order
def A226295(n): return n_order(prime(n), prime(n+1)) # Chai Wah Wu, Jun 15 2022

Crossrefs

Sequence in context: A253968 A102025 A309374 * A090127 A057910 A336066

Adjacent sequences: A226292 A226293 A226294 * A226296 A226297 A226298

Keyword

nonn

Author

Emmanuel Vantieghem, Jun 02 2013

Status

approved