Shouldn't sequence A036788 be keyworded "fini"?

Jonathan Post jvospost3 at gmail.com
Thu Jul 3 01:03:24 CEST 2008


Shouldn't sequence A036788 be keyworded "fini" for "finite"?

A036788  Length of Roman notation for n <= length of decimal representation.

Also, A036786, A036787.

This is because: "Once a number gets bigger than a few thousand, Roman
numerals become unwieldy. There are no 'bigger' symbols for 5000,
10,000 or a million. The Romans had two ways of writing bigger
numbers. They used what I call above 'deep parentheses' to multiply a
number by 1000. They were a C and a mirror image or upside down C and
I use normal parentheses to show them. Thus ( I ) is 1000 and ( X ) is
10,000. ( XXIII ) is 23,000. If you want to depict a million you can
use ( M ). Alternatively, the parentheses can be nested so ( I )  is
1,000 and  ( ( I ) ) is 1,000,000. The numbers can get a bit unwieldy
as they get bigger. An alternative way of depicting larger numbers was
to put a horizontal bar over the numeral, which multiplied it by
1000..."

http://www.web40571.clarahost.co.uk/roman/howtheywork.htm#larger

This has been, I hope, done correctly on:
A105269, A119310, A121305, and the like.

I spare you the mixed metaphor of:

Scrabble value of Roman numeral representation for the number n

which is easily calculated from (alphabetically sorted) by abuse of
"=" meaning when Scrabble-evaluated:
C = 3, D = 2, I = 1, L = 1, M = 3, V = 4, X = 8

as opposed to the (Roman-to-decimal evaluated)
I = 1
V = 5
X = 10
L = 50
C = 100
D = 500
M = 1000

Unless anyone wants to list the fixed points of the composition of
functions, i.e. the numbers beyond {1, 2, 3, ...} whose Scrabble
letter value of Roman numeral representation are equal to the
standard Roman-to-decimal evaluation? For instance, 9 -> IX -> (I = 1)
+ (X = 8) -> 9.





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