A335598 Squares that remain squares when the repunit with the same number of digits is added.

0, 25, 289, 2025, 13225, 100489, 198025, 319225, 466489, 4862025, 19758025, 42471289, 1975358025, 3199599225, 60415182025, 134885049289, 151192657225, 197531358025, 207612366025, 248956092025, 447136954489, 588186226489, 19753091358025, 31996727599225, 311995522926025, 1975308691358025

Offset: 1

Author

José de Jesús Camacho Medina, Jun 14 2020

Keywords

• nonn
• base
• easy

Examples

			0 is a term because 0 + 1 = 1. The result is another square.
25 is a term because 25 + 11 = 36. The result is another square.
289 is a term because 289 + 111 = 400. The result is another square.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002275, A048612, A273229.

Programs

Maple

f:= proc(d,q,m) local x,y;
if d < q/d then return NULL fi;
x:= ((d-q/d)/2)^2;
if x >= 10^m and x < 10^(m+1) then x else NULL fi;
end proc:
R:= 0:
for m from 1 to 20 do
  q:= (10^m-1)/9;
  V:= sort(convert(map(f, numtheory:-divisors(q),q,m-1),list));
  R:= R, op(V);
od:
R; # Robert Israel, Aug 21 2020

PARI

lista(limit)={for(k=0, sqrtint(limit), my(t=k^2); if(issquare(t + (10^if(t, 1+logint(t,10), 1)-1)/9), print1(t, ", ")))}
{ lista(10^12) } \\ Andrew Howroyd, Aug 11 2020

Extensions

Name corrected by Robert Israel, Aug 26 2020