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

[Chuck Seggelin]

I always thought bases larger than 10 use the first 10 digits first, and 
then use letters for the remaining digits.

So base 26 would be: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P

To encompass all 26 letters you'd use base 36.

Further, the sequence as described seems more like just the sums of the 
ordinal values of the letters in the name of each integer, except that z is 
treated as 0 instead of 26.  Because the terms are sums of letter values, 
you will get duplicates, as noted by the OP.

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
= 31104 + 828 + 14
= 31946

Giving the (starting from "one") sequence:

31946, 38760, 49537526, 732051, 724298, 36969, 47723135, 24375809, 1097258, 
38111, 882492287, 1807948346, 2310701170991, 1229565944111, 33766692143, 
62095095599, 80156542487855, 1137277763375, 1842973464623, 1807950886

Or if you want to replace the digits 0-9 with the letters A-J, giving 
base-26, you get the (starting from "one") sequence:

9806, 13430, 8817176, 97881, 93838, 12399, 8310185, 1972769, 234238, 12961, 
52636857, 235877906, 154869960141, 44729604621, 1642251533, 5666382189, 
3797555437325, 34673390765, 107041481053, 235879226

I think one can safely say that there is no possibility for a value 
appearing more than once in each of these sequences.

In neither case did I substitute Z for the 0 digit--the posted link on the 
matter appears to be a matter of opinion rather than principle, and Z being 
the 26'th letter, should represent the 26'th value (or 36'th if you prefer). 
The confusion arises because of leaving off the 10 digits.  If you begin 
with 0 and count up to 9, by the time you get to A there's no inner voice 
saying "but A is the first letter so it should be 1."

-- Chuck