cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A327894 Unicode codes for digit characters in the Basic Multilingual Plane (BMP).

Original entry on oeis.org

48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 1632, 1633, 1634, 1635, 1636, 1637, 1638, 1639, 1640, 1641, 1776, 1777, 1778, 1779, 1780, 1781, 1782, 1783, 1784, 1785, 1984, 1985, 1986, 1987, 1988, 1989, 1990, 1991, 1992, 1993, 2406, 2407, 2408, 2409, 2410, 2411, 2412, 2413, 2414, 2415, 2534
Offset: 1

Views

Author

Alonso del Arte, Sep 29 2019

Keywords

Comments

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.

Examples

			The following digits zero are encoded in the BMP (excluding Private Use Area).
U+0030 (48) [ISO-LATIN-1] Digit Zero
U+0660 (1632) Arabic-Indic Digit Zero
U+06F0 (1776) Extended Arabic-Indic Digit Zero
U+07C0 (1984) Nko Digit Zero
U+0966 (2406) Devanagari Digit Zero
U+09E6 (2534) Bengali Digit Zero
U+0A66 (2662) Gurmukhi Digit Zero
U+0AE6 (2790) Gujarati Digit Zero
U+0B66 (2918) Oriya Digit Zero
U+0BE6 (3046) Tamil Digit Zero
U+0C66 (3174) Telugu Digit Zero
U+0CE6 (3302) Kannada Digit Zero
U+0D66 (3430) Malayalam Digit Zero
U+0E50 (3664) Thai Digit Zero
U+0ED0 (3792) Lao Digit Zero
U+0F20 (3872) Tibetan Digit Zero
U+1040 (4160) Myanmar Digit Zero
U+1090 (4240) Myanmar Shan Digit Zero
U+17E0 (6112) Khmer Digit Zero
U+1810 (6160) Mongolian Digit Zero
U+1946 (6470) Limbu Digit Zero
U+19D0 (6608) New Tai Lue Digit Zero
U+1A80 (6784) Tai Tham Hora Digit Zero
U+1A90 (6800) Tai Tham Tham Digit Zero
U+1B50 (6992) Balinese Digit Zero
U+1BB0 (7088) Sundanese Digit Zero
U+1C40 (7232) Lepcha Digit Zero
U+1C50 (7248) Ol Chiki Digit Zero
U+A620 (42528) Vai Digit Zero
U+A8D0 (43216) Saurashtra Digit Zero
U+A900 (43264) Kayah Li Digit Zero
U+A9D0 (43472) Javanese Digit Zero
U+AA50 (43600) Cham Digit Zero
U+ABF0 (44016) Meetei Mayek Digit Zero
U+FF10 (65296) Fullwidth Digit Zero
Although U+3007, Ideographic Number Zero, from the CJK Symbols & Punctuation block, does have an associated numeric value of 0, it returns false for isDigit(). Thus 12295 is not included in this sequence.
		

Crossrefs

Programs

  • Scala
    (0 to 65535).filter(_.toChar.isDigit)

A380154 Golden numbers, for the years of the Metonic cycle. Assigned to the full moon days of the year with the standard pattern of a Runic calendar. Days without assignment are represented by zero.

Original entry on oeis.org

19, 8, 0, 16, 5, 0, 13, 2, 0, 10, 0, 18, 7, 0, 15, 4, 0, 12, 1, 0, 9, 0, 17, 6, 0, 14, 3, 0, 11, 19, 0, 8, 0, 16, 5, 0, 13, 2, 0, 10, 0, 18, 7, 0, 15, 4, 0, 21, 1, 0, 9, 0, 17, 6, 0, 14, 3, 0, 11, 19, 8, 0, 16, 5, 0, 13, 2, 0, 10, 0, 18, 7, 0, 15, 4, 0, 12, 1, 0, 9, 0, 17, 6, 0, 14, 3, 0, 11, 19, 0, 8, 0, 16, 5, 0, 13
Offset: 1

Views

Author

Thomas Scheuerle, Jan 13 2025

Keywords

Comments

The 19 year Metonic cycle repeats the pattern: 19,*,8,,16,5,,13,2,,10,,18,7,,15,4,,12,1,,9,,17,6,,14,3,,11. The gap marked with * alternates between odd and even cycles.
The alignment of the pattern is based on MS2913 from 1636. This is not accurate anymore in modern days as this pattern needs a shift of one day approximately every 304 years (Hipparchic cycle).
To each year the numbers from 1-19 where cyclically assigned. The positions of these numbers on the days of the year show the full moon for the corresponding year. Beware there are also calendar designs which track new moons with a cycle of 19 numbers.
The numbers are represented either by assigning runes from an extension of the Younger Futhark with three additional runic symbols or by the usage of Pentadic numerals. The latter is the case in MS2913.

Examples

			Note: In the original calendar usage no mapping on month and leap years was considered, instead the start of the year was determined by measuring the solstice each year. Days where originally numbered in 52 "weeks" of 7 days, however the counting restarted with 1 at each start of the year.
.
January
------------------------------------------------------------------
Day            1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14
Golden number 19| 8| 0|16| 5| 0|13| 2| 0|10| 0|18| 7| 0
------------------------------------------------------------------
Day           15|16|17|18|19|20|21|22|23|24|25|26|27|28|29|30|31
Golden number 15| 4| 0|12| 1| 0| 9| 0|17| 6| 0|14| 3| 0|11|19| 0
.
February
------------------------------------------------------------------
Day            1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14
Golden number  8| 0|16| 5| 0|13| 2| 0|10| 0|18| 7| 0|15
------------------------------------------------------------------
Day           15|16|17|18|19|20|21|22|23|24|25|26|27|28
Golden number  4| 0|12| 1| 0| 9| 0|17| 6| 0|14| 3| 0|11
.
March
------------------------------------------------------------------
Day            1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14
Golden number 19| 8| 0|16| 5| 0|13| 2| 0|10| 0|18| 7| 0
------------------------------------------------------------------
Day           15|16|17|18|19|20|21|22|23|24|25|26|27|28|29|30|31
Golden number 15| 4| 0|12| 1| 0| 9| 0|17| 6| 0|14| 3| 0|11|19| 0
.
April
------------------------------------------------------------------
Day            1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14
Golden number  8| 0|16| 5| 0|13| 2| 0|10| 0|18| 7| 0|15
------------------------------------------------------------------
Day            15|16|17|18|19|20|21|22|23|24|25|26|27|28|29|30
Golden number   4| 0|12| 1| 0| 9| 0|17| 6| 0|14| 3| 0|11|19| 8
.
May
------------------------------------------------------------------
Day            1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14
Golden number  0|16| 5| 0|13| 2| 0|10| 0|18| 7| 0|15| 4
------------------------------------------------------------------
Day            15|16|17|18|19|20|21|22|23|24|25|26|27|28|29|30|31
Golden number   0|12| 1| 0| 9| 0|17| 6| 0|14| 3| 0|11|19| 0| 8| 0
.
June
------------------------------------------------------------------
Day            1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14
Golden number 16| 5| 0|13| 2| 0|10| 0|18| 7| 0|15| 4| 0
------------------------------------------------------------------
Day            15|16|17|18|19|20|21|22|23|24|25|26|27|28|29|30
Golden number  12| 1| 0| 9| 0|17| 6| 0|14| 3| 0|11|19| 8| 0|16
.
July
------------------------------------------------------------------
Day            1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14
Golden number  5| 0|13| 2| 0|10| 0|18| 7| 0|15| 4| 0|12
------------------------------------------------------------------
Day            15|16|17|18|19|20|21|22|23|24|25|26|27|28|29|30|31
Golden number   1| 0| 9| 0|17| 6| 0|14| 3| 0|11|19| 0| 8| 0|16| 5
.
August
------------------------------------------------------------------
Day            1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14
Golden number  0|13| 2| 0|10| 0|18| 7| 0|15| 4| 0|12| 1
------------------------------------------------------------------
Day            15|16|17|18|19|20|21|22|23|24|25|26|27|28|29|30|31
Golden number   0| 9| 0|17| 6| 0|14| 3| 0|11|19| 8| 0|16| 5| 0|13
.
September
------------------------------------------------------------------
Day            1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14
Golden number  2| 0|10| 0|18| 7| 0|15| 4| 0|12| 1| 0| 9
------------------------------------------------------------------
Day            15|16|17|18|19|20|21|22|23|24|25|26|27|28|29|30
Golden number   0|17| 6| 0|14| 3| 0|11|19| 0| 8| 0|16| 5| 0|13
.
October
------------------------------------------------------------------
Day            1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14
Golden number  2| 0|10| 0|18| 7| 0|15| 4| 0|12| 1| 0| 9
------------------------------------------------------------------
Day            15|16|17|18|19|20|21|22|23|24|25|26|27|28|29|30|31
Golden number   0|17| 6| 0|14| 3| 0|11|19| 8| 0|16| 5| 0|13| 2| 0
.
November
------------------------------------------------------------------
Day            1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14
Golden number 10| 0|18| 7| 0|15| 4| 0|12| 1| 0| 9| 0|17
------------------------------------------------------------------
Day            15|16|17|18|19|20|21|22|23|24|25|26|27|28|29|30
Golden number   6| 0|14| 3| 0|11|19| 0| 8| 0|16| 5| 0|13| 2| 0
.
December
------------------------------------------------------------------
Day            1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14
Golden number 10| 0|18| 7| 0|15| 4| 0|12| 1| 0| 9| 0|17
------------------------------------------------------------------
Day            15|16|17|18|19|20|21|22|23|24|25|26|27|28|29|30|31
Golden number   6| 0|14| 3| 0|11|19| 8| 0|16| 5| 0|13| 2| 0|10| 0
.
Full moons in 2025:
((2025-5) mod 19) + 1 = 7.
This gives us the dates:
  13. January, 12. February, 13. March,
  12. April, 11. May, 10. June,
  9. July, 8. August, 6. September,
  6. October, 4. November, 4. December.
		

Crossrefs

Programs

  • PARI
    a(n) = {my(m = (n-1)%59 + 1); if(m >1, m++); [19, 0, 8, 0, 16, 5, 0, 13, 2, 0, 10, 0, 18, 7, 0, 15, 4, 0, 12, 1, 0, 9, 0, 17, 6, 0, 14, 3, 0, 11][(m-1)%30+1]}

Formula

Golden number (full moon) = ((year-5) mod 19) + 1. Example: 2025 gives 7.
There is also an estimation of new moon possible:
Golden number (new moon) = ((year-1) mod 19) + 1. Example: 2025 gives 11.
Note: The modern definition of the Golden numbers is (Year mod 19) + 1 for new moons, but we adapt here to the offset in MS2913.
a(n) = a(n-59).
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