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

franktaw at netscape.net franktaw at netscape.net
Wed Aug 26 23:01:51 CEST 2009

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:

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

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