[jud.mccranie at mindspring.com: Re: Status of Pollocks conjecture]

Olivier Gérard ogerard at ext.jussieu.fr
Wed Apr 18 11:40:50 CEST 2001

----- Forwarded message from Jud McCranie <jud.mccranie at mindspring.com> -----

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Reply-To: Jud McCranie <jud.mccranie at mindspring.com>
From: Jud McCranie <jud.mccranie at mindspring.com>
Subject:      Re: Status of Pollocks conjecture

At 11:58 PM 2/2/2001 -0500, Troy Kessler wrote:
>What is the status of Pollocks conjecture? It states that every number is
>the sum of at most 6 tetrahedral numbers. Has anyone worked on this
>recently? I know that many people have worked on sums of polygonal numbers.

Sloane's sequence A000797 implies that it is true (see below).  I
calculated some terms of the sequence below, but I don't know where the
"sufficient" part (or the finite nature of the sequence) came from.

%I A000797 M5033 N2172
%S A000797 17,27,33,52,73,82,83,103,107,137,153,162,217,219,227,237,247,258,
%T A000797
%N A000797 Not the sum of 4 tetrahedrals (a finite sequence).
%D A000797 H. E. Salzer and N. Levine, Table of integers not exceeding 10
00000 that are not expressible as the sum of four tetrahedral numbers,
Math. Comp., 12 (1958), 141-144.
%D A000797 The Algorithm Design Manual, Steven Skiena, section 2.7, page 43-44.
%K A000797 nonn,fini
%O A000797 1,1
%A A000797 njas
%E A000797 343867 is the 241st (and almost certainly the last) term. Five
tetrahedral numbers are necessary and sufficient to sum to the members of
this sequence - comments from Jud McCranie (jud.mccranie at mindspring.com).

|          Jud McCranie                                     |
|                                                           |
| Think recursively( Think recursively( Think recursively)) |

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