integer quadruples with all pairwise distances being squares

[Richard Mathar]

sequences reduces to 697 925 1073 1105 2165 2665 3277 3485 3965 4181 4225 4453
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Subject: Re: When d(m) = d(m+n) = n
Date: Sun, 20 Apr 2008 18:11:02 +0200
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>
> the following variation would be possible, though:
> d(a(n)) = 2n = d(a(n)+n)
>
> lq080419b(n,a)=n*=2;until(0,numdiv(a++)==n|next; numdiv(a+n\2)==n&break);a
> for(i=1,99,print1(lq080419b(i)", "))
> 2, 6, 172, 66, 15952, 84, 22592, 888, 2196, 3750,
>  *** numdiv: user interrupt after 20,719 ms.
>
> once again, for a(11) the going gets tough....
>

-- variation "d(a(n)) = 2n = d(a(n)+n)"

a(11) = 459932661
a(12) = ???
a(13) = 5547515219437003248294176693030899
a(17) = 1477350959671318879923111865392957430890479
a(19) > 7907^19

-- variation "d(a(n)) = 2n = d(a(n)+2n)"

a(11) > 7553167691293812663222804536362221219314843 = 7907^11

I tried, for the primes values of n , all possible a (n) = p_1 * p_2^n-1 , 
with p_i <= 999th-prime = 7907 .

regards,
JT

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