[seqfan] Re: Triangles of sums

hv at crypt.org hv at crypt.org
Mon Jul 26 17:10:17 CEST 2021


Allan Wechsler <acwacw at gmail.com> wrote:
:Returning to Recamán's original suggestion (entries must be prime or
:square), I wonder if anyone can quickly show a height-3 difference triangle
:with all square entries, or prove it impossible?

This was the smallest I found, testing only selected products of distinct
primes of the form 4k+1 as the square root of the apex:
    142129
  67600 74529
4096 63504 11025

(Roots: 377; 260, 273; 64, 252, 105.)

I imagine height-4 and above are also possible, but likely to be rather
harder to find. Maybe I'll give it a go: establishing least apex for
heights 3 and 4 would be enough to justify a sequence, I think, given
height 1 is degenerate and 2 is trivial.

Hugo


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