cp's OEIS Frontend

A237292 a(n) = A002326(2n(n+1)) / A002326(n).

%I A237292 #55 Jan 27 2016 17:46:07
%S A237292 1,3,5,7,9,11,13,15,17,19,7,23,25,27,29,31,33,35,37,13,41,43,45,47,49,
%T A237292 51,53,11,19,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,95,
%U A237292 97,99,101,103,35,107,109,37,113,115,117,119,121,123,125
%N A237292 a(n) = A002326(2n(n+1)) / A002326(n).
%C A237292 Note that ((2n+1)^2-1)/2 = 2n(n+1).
%C A237292 We have 1 <= a(n) <= 2n+1 and a(n) divides 2n+1 for every n >= 0.
%C A237292 Odd m is a Wieferich number A182297 if and only if a((m-1)/2) < m.
%C A237292 Odd prime p is a Wieferich prime A001220 if and only if a((p-1)/2) = 1.
%C A237292 a((n-1)/2) = 1 for n = 1, 1093, 3511, 7651, 10533, 14209, 17555, ...
%H A237292 Robert Israel, <a href="/A237292/b237292.txt">Table of n, a(n) for n = 0..10000</a>
%F A237292 a(n) = ord_{(2n+1)^2}(2) / ord_{2n+1}(2),  n >= 0.
%p A237292 1,seq(numtheory:-order(2,4*n*(n+1)+1)/numtheory:-order(2,2*n+1),n=1..100); # _Robert Israel_, Dec 02 2015
%o A237292 (PARI) a002326(n) = znorder(Mod(2, 2*n+1));
%o A237292 a(n) = a002326(2*n*(n+1))/a002326(n); \\ _Michel Marcus_, Feb 08 2014
%Y A237292 Cf. A001220, A002326, A077816 and A182297.
%K A237292 nonn
%O A237292 0,2
%A A237292 _Thomas Ordowski_, Feb 06 2014
%E A237292 More terms from _Michel Marcus_, Feb 08 2014
%E A237292 Edited by _Thomas Ordowski_, Dec 02 2015