A218712 - OEIS

%I #10 Jan 13 2025 11:33:09

%S 0,12,41,10133,34522,7745569,253879357,7986582530,61012922706,

%T 4563230639355,67972499239990,1330094199140593,47471944863682723,

%U 5000878909740249297,5000878909740249297,590115586441858677665,77072583141941801290876,423420364218752896284166

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

%H Robert Israel, <a href="/A218712/b218712.txt">Table of n, a(n) for n = 0..682</a>

%e a(4) = 34522 because 34522^2+1 =  5 * 29 ^ 4 * 337.

%p R:= 0,12: U:= [12,17]:

%p for n from 2 to 30 do

%p   qs:= map(u -> (u^2+1)/29^(n-1), U);

%p   ys:= [seq(-qs[i]/(2*U[i]) mod 29,i=1..2)];

%p   U:= U + ys*29^(n-1) mod 29^n;

%p   R:= R,min(U);

%p od:

%p R; # _Robert Israel_, Jan 13 2025

%t b=12;n29=29;jo=Join[{0,b},Table[n29=29*n29;b=PowerMod[b,29,n29];b=Min[b,n29-b],{99}]]

%Y Cf. A002522, A049532, A034939, A218709, A218710.

%K nonn

%O 0,2

%A _Michel Lagneau_, Nov 04 2012