# seq: Sum of base 26 values of the English name of n

Maximilian Hasler maximilian.hasler at gmail.com
Mon Jun 30 05:02:27 CEST 2008

```I agree to the given idea when speaking about "base",

On Sun, Jun 29, 2008 at 21:09, Chuck Seggelin
<seqfan at plastereddragon.com> wrote:
> Were I to treat "one" as a base-36 (or even a base-26) expression,
> the values represented by the letters would be affected by their position in the word.
> So "one" = O x 36^2 + N x 36^1 + E x 36^0
> Giving the (starting from "one") sequence:
> 31946, 38760, 49537526, 732051, 724298, 36969, 47723135, 24375809, 1097258,...

but this sequence is already there:

A072922   Spell English name for n, then interpret as number in base 36.

To avoid others losing time, I also copy what I sent earlier to NJAS & OP's :

On Sun, Jun 29, 2008 at 20:57, Maximilian Hasler  wrote:
>
> A073327                 Write English name for n (ignoring hyphens) and add
> numerical values of letters.
>        34, 58, 56, 60, 42, 52, 65, 49, 42, 39,
>
> I suggest to add here
> %Y A073327 Row sums of A073029
>
> and there
>
> %Y A073029 Cf. A073327 (row sums)
>
>> Well, I still have some reserves w.r.t. this sequence,
>> but what is nice/funny in the version you propose, is that a(0)=64 is
>> the offset giving the ASCII codes of the letters:
>> 'A' = 65
>> 'B' = 66
>> ...
>> Also, this could be defined as:
>> row sums of the fuzzy table seq.
>> A073029 Names for numbers in English, with each letter transformed
>> into its index in the alphabet.
>> 26,5,18,15,  /* zero */
>> 15,14,5, /*one*/
>> 20,23,15, /*two*/
>>
>> where row lengths  = A005589 = length of number NN spelled out in English
>>
>> Maximilian
>> PS: Neil, I once again suggest for the upcoming new version
>> that the "tabf" keyword should take an argument (in brackets or so)
>> which would give the seq. of row lengths such that clicking the "tabf"
>> keyw. would automatically display the table using data from the row
>> length seq.
>> i.e. it would look like:
>> KEYWORDS : nonn,tabf(A005589),
>> where "tabf" would be hyperlinked to .../table?a=NNN,b=5589&fmt=xxx
>> which would give the table of NNN with row lengths from A5589.

There was a flurry of activity on this topic last week.
I'm adding many of the resulting sequences to the OEIS - see A140481 onwards.
Neil

ma> From seqfan-owner at ext.jussieu.fr  Sun Jun 29 01:13:40 2008
ma> Date: Sat, 28 Jun 2008 16:12:26 -0700
ma> From: "Max Alekseyev" <maxale at gmail.com>
ma> To: SeqFan <seqfan at ext.jussieu.fr>
ma> Subject: extension to A006537 / A006538
ma>
ma> Would anybody like to extend A006537 / A006538 with the values from this paper:
ma> http://www.cs.uwaterloo.ca/research/tr/1996/21/cs-96-21.pdf
ma> and add it as a reference?
ma> ...

%I A006537 M0585
%S A006537 1,2,3,4,7,12,22,30,32,61,65,115,161,189,296,470,598,841,904,1856,2158,2416,
%T A006537 1925,3462,2130,3749,6546,11201,2159,2360,5186,6071,8664,14735,59745,68482,117997,
%U A006537 175672,268618,135585,178909,314752,490652,76800,116789,125493,290641,540539,831180
%N A006537 Worst cases for Pierce expansions (numerators).
%D A006537 P. Erdos and J. O. Shallit, New bounds on the length of finite Pierce and Engel
%D A006537 M. E. Mays, Iterating the division algorithm, Fib. Quart., 25 (1987), 204-213.
%H A006537 Vlado Keselj, <a href="http://www.cs.uwaterloo.ca/research/tr/1996/21/cs-96-21.pdf">Length of finite Pierce
%H A006537 <a href="http://www.research.att.com/~njas/sequences/Sindx_El.html#Engel">Index
%Y A006537 See A006538 for denominators.
%K A006537 nonn,frac
%O A006537 1,2
%A A006537 Jeffrey Shallit, njas
%E A006537 Added a(38)-a(49) from Keselj report, R. J. Mathar, Jun 30 2008.

%I A006538 M2471
%S A006538 1,3,5,11,11,19,35,47,53,95,103,179,251,299,503,743,1019,1319,1439,2939,3359,
%T A006538 3959,5387,5387,5879,5879,17747,17747,23399,23399,23399,23399,23399,23399,93596,
%U A006538 186479,186479,278387,442679,493919,493919,493919,830939,1371719,1371719,1371719,1371719,1371719,1371719
%N A006538 Worst cases for Pierce expansions (denominators).
%C A006538 See A006537 for numerators.
%D A006538 P. Erdos, J. O. Shallit, New bounds on the length of finite Pierce and Engel series.
%D A006538 M. E. Mays, Iterating the division algorithm, Fib. Quart., 25 (1987), 204-213.
%H A006538 Vlado Keselj, <a href="http://www.cs.uwaterloo.ca/research/tr/1996/21/cs-96-21.pdf">Length of finite Pierce
%H A006538 <a href="http://www.research.att.com/~njas/sequences/Sindx_El.html#Engel">Index
%K A006538 nonn,frac
%O A006538 1,2
%A A006538 Jeffrey Shallit, njas
%E A006538 Description corrected May 15 1995 and again Nov 07 2006.
%E A006538 Added a(38)-a(49) from Keselj report, R. J. Mathar, Jun 30 2008.

Yes. In this particular case, the partial sum is interesting in its own
right.

Drew

p.s. IMHO this is far more useful than any base-specific sequence.

On Jun 28 2008, Jonathan Post wrote:

>Number of self-avoiding walks on cubic lattice with no more than n steps.
>
>1, 7, 37, 187, 913, 4447, 21373, 102763, 490729, 2344615, 11154493,
>53088643, 251931385, 1195905895, 5664817573, 26839963627,
>126961839601, 600692091703, 2838415775797, 13414448995411,
>63331776834145, 299041867336303, 1410823850778709, 6656812065970123
>
>Formula
>Partial sum of A001412
>
>Offset
>0,2
>
>Example:
>a(9) = 1 + 6 + 30 + 150 + 726 + 3534 + 16926 + 81390 + 387966 +
>1853886 = 2344615
>
>Comment:
>Primes include a(1) = 7, a(2) = 37, a(5) = 4447, a(8) = 102763, a(15)
>= 26839963627.
>
>Cf. A001412, A002902, A078717, A001411, A001413.
>
>Keywords:
>nonn,walk
>
>Not all partial sums are desired, but this one seems natural and
>non-arbitrary to me.  Anyone find this worth submitting?
>
>Best,
>
>Jonathan Vos Post
>

```