Each number in this table has a significance, and it is not just the property of the individual number.

What statement might define the right for each to appear?

1 1 1 2 4 4 3 9 9 13 169 16 67 4489 25 264 69696 36 1667 2778889 49 .. ... 64

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That said, is it possible (and how) to analytically define the precise numerical values of successive rows?

A quick mathematica program gave the first 10 rows of the table which is a list of the integers for which when you add all the digits in  their square you get the next perfect square.  i.e 13^2=169 1+6+9=16 so then next row would have digital sum of 25 and thus 67^2=4489 4+4+8+9=25

i=1;

src=1;

While[src£10,

n=i^2;

ds=Total[IntegerDigits[n]];

If[dsŠsrc^2,

Print[i," ",n," ",src^2];

src++;

];

i++;

];

and this gives

1 1 1

2 4 4

3 9 9

13 169 16

67 4489 25

264 69696 36

1667 2778889 49

16667 277788889 64

94863 8998988769 81

1643167 2699997789889 100

 

Posted by Daniel on 2009-02-22 14:23:49