A260305 We represent square arrays of single-digit entries by the single number formed by reading them row-by-row, top-to-bottom. Sequence gives list of k X k square grids formed from single-digit numbers having property that reading across each row and each column gives a square number.

1, 4, 9, 1664, 3664, 6449, 8116, 121256169, 121289196, 144400400, 144484441, 169676961, 361676169, 441400100, 441484144, 529256961, 729256961, 841400100, 841484144, 961676169, 1296202592166561, 1369384464009409

Offset

1,2

Comments

Suppose for example a term has 9 digits, say abcdefghi. This means that the grid is

abc

def

ghi

and that the decimal concatenations abc, def, ghi, adg, beh, cfi are all squares. E.g., for 121256169 we see that 121, 256, 169, 121, 256 and 169 are squares.

There are 3 grids of size 1 X 1.

There are 4 grids of size 2 X 2.

There are 13 grids of size 3 X 3.

There are 14 grids of size 4 X 4.

There are 76 grids of size 5 X 5.

There are 108 grids of size 6 X 6.

There are 459 grids of size 7 X 7.

There are 844 grids of size 8 X 8.

No leading zeros are allowed in the rows and columns.

Links

Luca Petrone, Table of n, a(n) for n = 1..1521

Example

169676961 is in the sequence, so the 3 X 3 grid is:
(1 6 9)
(6 7 6)
(9 6 1)
146414494469696449441461 is in the sequence; this is a 25-digit term, and the 5 X 5 grid is:
(1 4 6 4 1)
(4 4 9 4 4)
(6 9 6 9 6)
(4 4 9 4 4)
(1 4 6 4 1)

Crossrefs

Cf. A105074.

Sequence in context: A073172 A168139 A258660 * A229338 A111443 A299118

Adjacent sequences: A260302 A260303 A260304 * A260306 A260307 A260308

Keyword

nonn,base

Author

Pieter Post, Nov 10 2015

Extensions

Corrected and extended by Luca Petrone, Jan 08 2017

Status

approved