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A218712 a(n) is the smallest number such that a(n)^2 + 1 is divisible by 29^n.

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%I A218712 #10 Jan 13 2025 11:33:09
%S A218712 0,12,41,10133,34522,7745569,253879357,7986582530,61012922706,
%T A218712 4563230639355,67972499239990,1330094199140593,47471944863682723,
%U A218712 5000878909740249297,5000878909740249297,590115586441858677665,77072583141941801290876,423420364218752896284166
%N A218712 a(n) is the smallest number such that a(n)^2 + 1 is divisible by 29^n.
%H A218712 Robert Israel, <a href="/A218712/b218712.txt">Table of n, a(n) for n = 0..682</a>
%e A218712 a(4) = 34522 because 34522^2+1 =  5 * 29 ^ 4 * 337.
%p A218712 R:= 0,12: U:= [12,17]:
%p A218712 for n from 2 to 30 do
%p A218712   qs:= map(u -> (u^2+1)/29^(n-1), U);
%p A218712   ys:= [seq(-qs[i]/(2*U[i]) mod 29,i=1..2)];
%p A218712   U:= U + ys*29^(n-1) mod 29^n;
%p A218712   R:= R,min(U);
%p A218712 od:
%p A218712 R; # _Robert Israel_, Jan 13 2025
%t A218712 b=12;n29=29;jo=Join[{0,b},Table[n29=29*n29;b=PowerMod[b,29,n29];b=Min[b,n29-b],{99}]]
%Y A218712 Cf. A002522, A049532, A034939, A218709, A218710.
%K A218712 nonn
%O A218712 0,2
%A A218712 _Michel Lagneau_, Nov 04 2012