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

1,2

Links

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

Example

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.

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

Prog

(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

Crossrefs

Cf. A002275, A048612, A273229.

Sequence in context: A351925 A029987 A017582 * A210430 A158990 A079873

Adjacent sequences: A335595 A335596 A335597 * A335599 A335600 A335601

Keyword

nonn,base,easy

Author

José de Jesús Camacho Medina, Jun 14 2020

Extensions

Name corrected by Robert Israel, Aug 26 2020

Status

approved