A236383 - OEIS

%I #19 Jun 25 2019 01:33:42

%S 428,453,465,381,369,358,917,421,394,452,704,716,442,833,323,380,347,

%T 697,8376,449,3994,407,439,431,4770,6961,391,336,3533,4277,7915,36332,

%U 7705,4487,3323,8869,8942,3250,4560,7632,90951,7988,4204,3606,8586,72774

%N Smallest k such that k^2 is a concatenation of two numbers x and y where y = x + n^2 and x and y have the same number of digits.

%C Conjecture: a(n) exists for all numbers n.

%C a(1) = A030467(1).

%C The same problem with the concatenation of x + n instead of x + n^2 is difficult.

%C The corresponding sequence with x + n instead of x + n^2 starts with 36363636364, 428, 8874, 5, 310, 7, 39 for n = 0,...,6, and a(7) > 10^70, if it exists. - _Giovanni Resta_, Jun 24 2019

%H Michel Lagneau, <a href="/A236383/b236383.txt">Table of n, a(n) for n = 1..245</a>

%e a(11) = 704 because 704^2 = 495616 is the concatenation of 495 and 616, and 616 - 495 = 121 = 11^2.

%p for n from 1 to 47 do:

%p    ii:=0:

%p       for k from 1 to 10^7 while(ii=0)do :

%p          x:=convert(k^2,base,10):n1:=nops(x):

%p          if irem(n1,2)=0

%p            then

%p            s:=sum('x[i]*10^(i-1) ', 'i'=1..n1/2):

%p            z:=convert(s,base,10):

%p            s1:=sum('x[j]*10^(j-n1/2-1) ', 'j'=n1/2+1..n1):

%p             if s-s1 = n^2

%p             then

%p             ii:=1:printf(`%d, `,k):

%p             else

%p             fi:

%p          fi:

%p        od:

%p    od:

%Y Cf. A030467.

%K nonn,base

%O 1,1

%A _Michel Lagneau_, Jan 24 2014

%E Definition corrected by _Giovanni Resta_, Jun 24 2019