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?

(In reply to re: computer solution by brianjn)

The comparison for the while is <= and for the If is ==.   I think the problem arose from me simply copying and pasting directly from Mathematica, I've had problems with that in the past.  I rewrote the code below, hopefully it is more readable

i=1;
src=1;
While[src<=10,
n=i^2;
ds=Total[IntegerDigits[n]];
If[ds==src^2,
Print[i," ",n," ",src^2];
src++;
];
i++;
];

Posted by Daniel on 2009-02-23 10:08:19