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

%I A226367 #14 May 23 2024 22:02:42
%S A226367 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,
%T A226367 100,51,106,18,28,7,130,68,46,148,150,156,81,83,43,178,180,95,48,196,
%U A226367 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
%N A226367 Multiplicative order of the (n+1)-st prime modulo the n-th prime.
%C A226367 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).
%H A226367 Alois P. Heinz, <a href="/A226367/b226367.txt">Table of n, a(n) for n = 1..20000</a>
%e A226367 a(2) = 2 because 5^2 == 1 (mod 3) but 5^1 !== 1(mod 3).
%e A226367 a(6) = 6  because 17^6 == 1 (mod 13) but 17^u !== 1 (mod 13) for  u < 6.
%t A226367 Table[MultiplicativeOrder[Prime[n+1],Prime[n]],{n,1,75}]
%o A226367 (PARI) vector(80, n, p = prime(n); znorder(Mod(nextprime(p+1), p))) \\ _Michel Marcus_, Feb 09 2015
%Y A226367 Cf. A226295 (multiplicative order of p(n) mod p(n+1)).
%K A226367 nonn
%O A226367 1,2
%A A226367 _Emmanuel Vantieghem_, Jun 05 2013