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

%I A226295 #18 Jun 16 2022 00:09:58
%S A226295 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,
%T A226295 102,106,36,7,63,130,136,69,148,30,156,54,166,86,89,180,190,96,49,198,
%U A226295 7,111,226,76,58,34,24,25,256,262,67,270,276,70,47,73,153,310
%N A226295 Multiplicative order of the n-th prime modulo the (n+1)th prime.
%C A226295 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.
%H A226295 Charles R Greathouse IV, <a href="/A226295/b226295.txt">Table of n, a(n) for n = 1..10000</a>
%H A226295 K. Kashihara, <a href="http://www.gallup.unm.edu/~smarandache/Kashihara.pdf">Comments and Topics on Smarandache Notions and Problems</a>, Erhus University Press, 1996, 50 pages. See page 44.
%H A226295 K. Kashihara, <a href="/A011772/a011772.pdf">Comments and Topics on Smarandache Notions and Problems</a>, Erhus University Press, 1996, 50 pages. [Cached copy] See page 44.
%e A226295 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.
%t A226295 Table[MultiplicativeOrder[Prime[n], Prime[n+1]], {n,80}]
%o A226295 (PARI) a(n)=my(p=prime(n));znorder(Mod(p,nextprime(p+1))) \\ _Charles R Greathouse IV_, Jun 04 2013
%o A226295 (Python)
%o A226295 from sympy import prime, n_order
%o A226295 def A226295(n): return n_order(prime(n),prime(n+1)) # _Chai Wah Wu_, Jun 15 2022
%K A226295 nonn
%O A226295 1,1
%A A226295 _Emmanuel Vantieghem_, Jun 02 2013