cp's OEIS Frontend

Comment from Antti Karttunen, Sep 05 2004: (Start)

Also number of characters needed to write the number n in classical Greek alphabetic system, up to n=999. The Greek alphabetic system assigned values to the letters as follows:

alpha = 1, beta = 2, gamma = 3, delta = 4, epsilon = 5, digamma = 6, zeta = 7, eta = 8, theta = 9, iota = 10, kappa = 20, lambda = 30, mu = 40, nu = 50, xi = 60, omicron = 70, pi = 80, koppa = 90, rho = 100, sigma = 200, tau = 300, upsilon = 400, phi = 500, chi = 600, psi = 700, omega = 800, sampi = 900. (End)

For partial sums see A102685. - Hieronymus Fischer, Jun 06 2012

This order of runes with these graphic forms is used in many rune staves in the collections of the National Museum of Finland. Note that the first sixteen of them make up the so-called younger futhark (runic alphabet), but with the fourteenth and fifteenth runes (codes 5850 and 5848, i.e. ᛚ ᛚ (L) ᛘ ᛘ (M)) having swapped their places from the usual m-l order:

ᚠ (F), ᚢ (U), ᚦ (Th), ᚭ (O), ᚱ (R), ᚴ (K), ᚼ (H), ᚿ (N), ᛁ (I), ᛆ (A), ᛋ (S), ᛏ (T), ᛒ (B), ᛚ (L), ᛘ (M), ᛦ (Y); or, using html character entities:

ᚠ (F), ᚢ (U), ᚦ (Th), ᚭ (O), ᚱ (R), ᚴ (K), ᚼ (H), ᚿ (N),

ᛁ (I), ᛆ (A), ᛋ (S), ᛏ (T), ᛒ (B), ᛚ (L), ᛘ (M), ᛦ (Y).

The last three lunation runes were ligatures, coined to make up the full 1-19 set: ᛮ ᛮ (ARLAUG), ᛯ ᛯ (TVIMADUR), ᛰ ᛰ (BELGTHOR).

A digit is a character in a given Unicode block that can be combined with other digits in that same Unicode block to form zero-padded nonnegative integers in a positional number base, which can then be sorted arithmetically according to their Unicode values.

That's not the case for numerals, such as for example Roman Numeral Ten (U+2169), nor ASCII letters used as Roman numerals. For example, XIV, XVI, XIX would be sorted as XIV, XIX, XVI (14, 19, 16, rather than 14, 16, 19).

This listing does not include digit characters in the BMP Private Use Area, such as, for example, Klingon Digit Zero (U+F8F0, corresponding to 63728) as assigned by ConScript.

Unicode consistently assigns digit characters so that the code point modulo 16 corresponds to the numerical value of the digit, so that digit zero is U+xxx0 and digit nine is U+xxx9.

Except for the digits for Indian languages and the Limbu language, which are assigned so that the code point modulo 16 corresponds to the numerical value of the digit plus 6 (thus digit zero is U+xxx6 and digit nine is U+xxxF).

This is a principle that ConScript for the most part follows, such as for example with Klingon and Ferengi. Perhaps the only exception is U+E033, Tengwar Letter Stemless Vilya which also serves as Tengwar Digit One. Interestingly, however, take note of Tengwar Duodecimal Digit Ten (U+E06A) and Tengwar Duodecimal Digit Eleven (U+E06B).

The largest number that could theoretically be in this sequence is 65535. There are digits in the supplementary planes, e.g. Osmanya Digit Zero, U+104A0, giving a theoretical maximum of 1114111.

However, since the assignment of the supplementary planes is ongoing for many years to come, to include those in this entry might require occasional insertions. Computation of that sequence would pose only one minor and easily solved problem for Java's isDigit() function, though.

On the other hand, the assignment of Arabic Extended-B (U+0870 through U+089F) has not been finalized yet, though that proposal contains neither digits nor numerals.

Also, no proposal nor suggestion has been made for U+2FE0 through U+2FEF, so there is a small chance those could be assigned digits.