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

Jonathan Post jvospost3 at gmail.com
Sun Jun 29 23:32:25 CEST 2008

```After several times in a row that njas kindly encouraged me to submit,
or directly accepted, several elegant or from-literature sequences of
mine, I'm almost embarrassed to suggest this one. I've earlier termed
such as this: "swimming in the shallow end of the pool."

But it is extremely elementary, which can be good, even though base
and word, which some find bad.  Since I expect to be teaching at a
specific charter school as of August, I often think of how to use and
augment OEIS to be useful to American high school students and
remedial students and challenged students and dyscalculia-plagued
students (understanding that many other countries have median students

Sum of base 26 values of the English name of n, excluding spaces and hyphens.
n   a(n) comment
0   38    z(base 26)+e(base 26)+r(base 26)+o(base 26) = 0+5+18+15 = 38
1   34    o+n+e = 15+14+5 = 34
2   58    t+w+o = 20+23+15
3   56
4   60
5   42
6   52
7   65
8   49
9   42    same value as a(5)
10  39   t+e+n = 20+5+14
11  63
12  87
13  99   note that "teen" --> 44, so a(Xteen)=a(X)+44
14  104
15  65   same value as a(7)
16  96
17  109
18  93
19  66
20  107  t+w+e+n+t+y = 20+23+5+14+20+25, so a(twentyX)=107+a(X)
21  141
22  165
23  163
24  167
25  149
26  159
27  172
28  156
29  149  same value as a(25)
30  100  t+h+i+r+t+y = 20+8+9+18+20+25, so a(thirtyX)=100+a(X)

and so forth.

The usual questions: what are the fixed points of the function?  What
is the behavior on iteration besides at the fixed points (i.e. what
cycles, what attractors)? What values have more than one inverse
image? What values appear (sorted) versus what values never appear?
And, of course, what is the equivalent in other languages and
alphabets?

Again, this may be ugly to some readers, but a child can build the
tables needed for table look-up and compute values quickly, which is
an entry to teaching the mathematical distinctions between a number
and the name(s) of a number, and of the concept of function.

Does anyone find this interesting enough to code, check, extend?

Best,

Jonathan Vos Post

comment: the number of terms in the sum is A005589(n).

```