A335598 - OEIS

%I #26 Aug 27 2020 08:18:41

%S 0,25,289,2025,13225,100489,198025,319225,466489,4862025,19758025,

%T 42471289,1975358025,3199599225,60415182025,134885049289,151192657225,

%U 197531358025,207612366025,248956092025,447136954489,588186226489,19753091358025,31996727599225,311995522926025,1975308691358025

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

%H Robert Israel, <a href="/A335598/b335598.txt">Table of n, a(n) for n = 1..10000</a>

%e 0 is a term because 0 + 1 = 1. The result is another square.

%e 25 is a term because 25 + 11 = 36. The result is another square.

%e 289 is a term because 289 + 111 = 400. The result is another square.

%p f:= proc(d,q,m) local x,y;

%p if d < q/d then return NULL fi;

%p x:= ((d-q/d)/2)^2;

%p if x >= 10^m and x < 10^(m+1) then x else NULL fi;

%p end proc:

%p R:= 0:

%p for m from 1 to 20 do

%p   q:= (10^m-1)/9;

%p   V:= sort(convert(map(f, numtheory:-divisors(q),q,m-1),list));

%p   R:= R, op(V);

%p od:

%p R; # _Robert Israel_, Aug 21 2020

%o (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 { lista(10^12) } \\ _Andrew Howroyd_, Aug 11 2020

%Y Cf. A002275, A048612, A273229.

%K nonn,base,easy

%O 1,2

%A _José de Jesús Camacho Medina_, Jun 14 2020

%E Name corrected by _Robert Israel_, Aug 26 2020