Scrabblomics; COMMENT FROM Jonathan Vos Post RE A113172

[Jonathan Post]

Here's more fun, with a silly if plausibly motivated name.

Subject: NEW SEQUENCE FROM Jonathan Vos Post


%I A000001
%S A000001 1,
3, 3,
8, 10, 8,
9, 12, 12, 9,
4, 15, 19, 15, 4,
7, 15, 19, 19, 15, 7,
8, 18, 19, 21, 19, 18, 8,
9, 22, 20, 11, 11, 20, 22, 9,
4, 15, 17, 15, 18, 15, 17, 15, 4,
7, 15, 18, 18, 20, 20, 18, 18, 15, 7,
8, 18, 20, 22, 21, 11, 21, 22, 20, 18, 8,
9, 22, 21, 17, 19, 18, 18, 19, 17, 21, 22, 9
%N A000001 Pascrabble Triangle, by rows.
%C A000001 The apex of the triangle is 1.  Any other value is the
Scrabble value of English name for the number which is the sum of the
numbers above. This is generated the same way as A007318 Pascal's
triangle read by rows, except apply A113172 to each sum. The first
column of this triangle is 1, 3, 8, 9, 4, 7, 8, 9, 4, 7, 8, 9, 4, 7...
= iterations 1, A113172(1), A113172(A113172(1)),
A113172(A113172(A113172(1))).
The central pascrabble numbers T(2n+1,n) = 1, 10, 19, 21, 18, 11, 22, ...
%F A000001 T(1,1) = 1; for i > 1, T(i,j) = A113172(T(i-1, j-1)+T(i-1, j).
%e A000001 Triangle begins:
row.|.values in row
.1..|01
.2..|03.03
.3..|08.10.08
.4..|09.12.12.09
.5..|04.15.19.15.04
.6..|07.15.19.19.15.07
.7..|08.18.19.21.19.18.08
.8..|09.22.20.11.11.20.22.09
.9..|04.15.17.15.18.15.17.15.04
10..|07.15.18.18.20.20.18.18.15.07
11..|08.18.20.22.21.11.21.22.20.18.8
12..|09.22.21.17.19.18.18.19.17.21.22.09
%Y A000001 cf. A007318 Pascal's triangle read by rows, A113172.
%O A000001 1
%K A000001 ,easy,nonn,tabl,word,
%A A000001 Jonathan Vos Post (jvospost2 at yahoo.com), Nov 08 2006

I think that this cut & paste is pure text, and not HTML (as Olivier asked)
but I am not sure.

On 11/8/06, jonathan post <jvospost2 at yahoo.com> wrote:
>
> My backup copy (as no autoreply yet).
>
> Subject: COMMENT FROM Jonathan Vos Post RE A113172
>
>
> %I A113172
> %S A113172
> 13,3,6,8,7,10,10,8,9,4,3,9,12,11,11,13,14,12,12,8,12,15,18,20,19,22,22
> %N A113172 Scrabble value of English word for the
> number n.
> %C A113172 Is 12 the unique fixed point of Scrabble
> value of English word for the number n, where
> A113172(n) = n? 12 --> "TWELVE" --> 1+4+1+1+4+1 -->
> 12. For what n are A113172(n) prime? For what n are
> there cycles of what length for iterations n,
> A113172(n), A113172(A113172(n)),
> A113172(A113172(A113172(n))), ...? For what n does
> A113172(n) | n? These are key questions in general
> Scrabblomics.
> %F A113172 Scrabble value of English word for the
> number n.
> %O A113172 1
> %K A113172 ,easy,nonn,word,
> %A A113172 Jonathan Vos Post (jvospost2 at yahoo.com),
> Nov 08 2006
>
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