login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A236383 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. 2
428, 453, 465, 381, 369, 358, 917, 421, 394, 452, 704, 716, 442, 833, 323, 380, 347, 697, 8376, 449, 3994, 407, 439, 431, 4770, 6961, 391, 336, 3533, 4277, 7915, 36332, 7705, 4487, 3323, 8869, 8942, 3250, 4560, 7632, 90951, 7988, 4204, 3606, 8586, 72774 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

a(1) = A030467(1).

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

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

LINKS

Michel Lagneau, Table of n, a(n) for n = 1..245

EXAMPLE

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

MAPLE

for n from 1 to 47 do:

   ii:=0:

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

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

         if irem(n1, 2)=0

           then

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

           z:=convert(s, base, 10):

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

            if s-s1 = n^2

            then

            ii:=1:printf(`%d, `, k):

            else

            fi:

         fi:

       od:

   od:

CROSSREFS

Cf. A030467.

Sequence in context: A251147 A095811 A235217 * A224668 A030467 A253505

Adjacent sequences:  A236380 A236381 A236382 * A236384 A236385 A236386

KEYWORD

nonn,base

AUTHOR

Michel Lagneau, Jan 24 2014

EXTENSIONS

Definition corrected by Giovanni Resta, Jun 24 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 15 21:37 EST 2019. Contains 329168 sequences. (Running on oeis4.)