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

0, 12, 41, 10133, 34522, 7745569, 253879357, 7986582530, 61012922706, 4563230639355, 67972499239990, 1330094199140593, 47471944863682723, 5000878909740249297, 5000878909740249297, 590115586441858677665, 77072583141941801290876, 423420364218752896284166

Offset: 0

Author

Michel Lagneau, Nov 04 2012

Keywords

• nonn

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 0..682

Crossrefs

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

Programs

Maple

R:= 0,12: U:= [12,17]:
for n from 2 to 30 do
  qs:= map(u -> (u^2+1)/29^(n-1), U);
  ys:= [seq(-qs[i]/(2*U[i]) mod 29,i=1..2)];
  U:= U + ys*29^(n-1) mod 29^n;
  R:= R,min(U);
od:
R; # Robert Israel, Jan 13 2025

Mathematica

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