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A335598
Squares that remain squares when the repunit with the same number of digits is added.
1
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
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
KEYWORD
nonn,base,easy
AUTHOR
EXTENSIONS
Name corrected by Robert Israel, Aug 26 2020
STATUS
approved