login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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