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A372801 Order of 16 modulo the n-th prime: least k such that prime(n) divides 16^k-1.

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%I A372801 #13 May 13 2024 15:36:19
%S A372801 1,1,3,5,3,2,9,11,7,5,9,5,7,23,13,29,15,33,35,9,39,41,11,12,25,51,53,
%T A372801 9,7,7,65,17,69,37,15,13,81,83,43,89,45,95,24,49,99,105,37,113,19,29,
%U A372801 119,6,25,4,131,67,135,23,35,47,73,51,155,39,79,15,21,173,87,22,179
%N A372801 Order of 16 modulo the n-th prime: least k such that prime(n) divides 16^k-1.
%C A372801 a(n) is the period of the expansion of 1/prime(n) in hexadecimal.
%H A372801 Jianing Song, <a href="/A372801/b372801.txt">Table of n, a(n) for n = 2..10000</a>
%F A372801 a(n) = A014664(n)/gcd(4, A014664(n)) = A082654(n)/gcd(2, A082654(n)).
%F A372801 a(n) <= (prime(n) - 1)/2.
%o A372801 (PARI) a(n) = znorder(Mod(16, prime(n))).
%Y A372801 Cf. A302141 (order of 16 mod 2n+1).
%Y A372801 In other bases: A014664, A062117, A082654, A211241, A211242, A211243, A211244, A211245, A002371.
%K A372801 nonn,easy
%O A372801 2,3
%A A372801 _Jianing Song_, May 13 2024