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A226295
Multiplicative order of the n-th prime modulo the (n+1)th prime.
4
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
KEYWORD
nonn
AUTHOR
Emmanuel Vantieghem, Jun 02 2013
STATUS
approved