[seqfan] Re: A135412

Don Reble djr at nk.ca
Fri Aug 19 22:10:00 CEST 2016


> The Name is: Integers that are Heronian means of two distinct
> nonnegative integers. Data:
> 3, 6, 7, 9, 12, 13, 14, 15, 18, 19, 21, 24, 26, 27, 28, 30, 31, 33, 35, ...

> The Comment is: If "nonnegative" is changed to "positive", most numbers
> divisible by 3 drop out of the sequence. 

> But if 0's are allowed, why isn't every positive integer in this
> sequence? n is the Heronian mean of 0 and 3*n.

    I also find the Name and Comment baffling.

> the given Data seems to match a different sequence: ...
> n is in the sequence iff there exist distinct integers r1, r2, r3 such
> that r1 + r2 + r3 = n and r1 r2 + r1 r3 + r2 r3 = 0.

    Perhaps it's "three non-zero integers", so that n,0,0 -> n
    doesn't happen, but 2n,2n,-n -> 3n does happen.
    (But also 20,5,-4 yields 21.)

    The sequence might be A050931 plus multiples of 3,
    but I like Robert's take better.

-- 
Don Reble  djr at nk.ca



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