[seqfan] Re: (Not)Possible values of sod of squares

[franktaw at netscape.net]

As shown, 27 can be the sod of a square.

As David Wilson commented, the constraint is merely that the sod must 
be a square mod 9: 0, 1, 4, or 7.  It is not obvious that every number 
of this form can be obtained, but this is almost certainly true.

It is true any square can be obtained (in any base 3 or more): just put 
n 1's in positions such that there are no duplicate pair sums: e.g., 
1001011 for n=4 (generally, you can use A000071 for the positions).

Franklin T. Adams-Watters

-----Original Message-----
From: zak seidov <zakseidov at yahoo.com>

Dear seqfans,

The list of minimal m with sod(m^2)=n:
{n,m}:
...,{27,63}...

Not all n's<148 are present.
Values of n which are multiples of 3^(2k+1) (odd powers of 3: 3,27,243) 
can not
be sod of squares
...