cp's OEIS Frontend

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

%I A335598 #26 Aug 27 2020 08:18:41
%S A335598 0,25,289,2025,13225,100489,198025,319225,466489,4862025,19758025,
%T A335598 42471289,1975358025,3199599225,60415182025,134885049289,151192657225,
%U A335598 197531358025,207612366025,248956092025,447136954489,588186226489,19753091358025,31996727599225,311995522926025,1975308691358025
%N A335598 Squares that remain squares when the repunit with the same number of digits is added.
%H A335598 Robert Israel, <a href="/A335598/b335598.txt">Table of n, a(n) for n = 1..10000</a>
%e A335598 0 is a term because 0 + 1 = 1. The result is another square.
%e A335598 25 is a term because 25 + 11 = 36. The result is another square.
%e A335598 289 is a term because 289 + 111 = 400. The result is another square.
%p A335598 f:= proc(d,q,m) local x,y;
%p A335598 if d < q/d then return NULL fi;
%p A335598 x:= ((d-q/d)/2)^2;
%p A335598 if x >= 10^m and x < 10^(m+1) then x else NULL fi;
%p A335598 end proc:
%p A335598 R:= 0:
%p A335598 for m from 1 to 20 do
%p A335598   q:= (10^m-1)/9;
%p A335598   V:= sort(convert(map(f, numtheory:-divisors(q),q,m-1),list));
%p A335598   R:= R, op(V);
%p A335598 od:
%p A335598 R; # _Robert Israel_, Aug 21 2020
%o A335598 (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, ", ")))}
%o A335598 { lista(10^12) } \\ _Andrew Howroyd_, Aug 11 2020
%Y A335598 Cf. A002275, A048612, A273229.
%K A335598 nonn,base,easy
%O A335598 1,2
%A A335598 _José de Jesús Camacho Medina_, Jun 14 2020
%E A335598 Name corrected by _Robert Israel_, Aug 26 2020