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.

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.

This page as a plain text file.
%I A380154 #48 Jan 27 2025 21:15:16
%S A380154 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,
%T A380154 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,
%U A380154 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
%N 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.
%C A380154 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.
%C A380154 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).
%C A380154 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.
%C A380154 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.
%H A380154 The Schoyen Collection, <a href="https://www.schoyencollection.com/calendars-almanacs/folding-calendars/norwegian-girdle-calendar-ms-2913">MS2913 Norwegian girdle calendar</a>.
%H A380154 Wikipedia, <a href="https://en.wikipedia.org/wiki/Runic_calendar">Runic calendar</a>.
%H A380154 <a href="/index/Ca#calendar">Index entries for sequences related to calendars</a>
%H A380154 <a href="/index/Rec#order_59">Index entries for linear recurrences with constant coefficients</a>,signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).
%F A380154 Golden number (full moon) = ((year-5) mod 19) + 1. Example: 2025 gives 7.
%F A380154 There is also an estimation of new moon possible:
%F A380154   Golden number (new moon) = ((year-1) mod 19) + 1. Example: 2025 gives 11.
%F A380154 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.
%F A380154 a(n) = a(n-59).
%e A380154 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.
%e A380154 .
%e A380154 January
%e A380154 ------------------------------------------------------------------
%e A380154 Day            1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14
%e A380154 Golden number 19| 8| 0|16| 5| 0|13| 2| 0|10| 0|18| 7| 0
%e A380154 ------------------------------------------------------------------
%e A380154 Day           15|16|17|18|19|20|21|22|23|24|25|26|27|28|29|30|31
%e A380154 Golden number 15| 4| 0|12| 1| 0| 9| 0|17| 6| 0|14| 3| 0|11|19| 0
%e A380154 .
%e A380154 February
%e A380154 ------------------------------------------------------------------
%e A380154 Day            1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14
%e A380154 Golden number  8| 0|16| 5| 0|13| 2| 0|10| 0|18| 7| 0|15
%e A380154 ------------------------------------------------------------------
%e A380154 Day           15|16|17|18|19|20|21|22|23|24|25|26|27|28
%e A380154 Golden number  4| 0|12| 1| 0| 9| 0|17| 6| 0|14| 3| 0|11
%e A380154 .
%e A380154 March
%e A380154 ------------------------------------------------------------------
%e A380154 Day            1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14
%e A380154 Golden number 19| 8| 0|16| 5| 0|13| 2| 0|10| 0|18| 7| 0
%e A380154 ------------------------------------------------------------------
%e A380154 Day           15|16|17|18|19|20|21|22|23|24|25|26|27|28|29|30|31
%e A380154 Golden number 15| 4| 0|12| 1| 0| 9| 0|17| 6| 0|14| 3| 0|11|19| 0
%e A380154 .
%e A380154 April
%e A380154 ------------------------------------------------------------------
%e A380154 Day            1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14
%e A380154 Golden number  8| 0|16| 5| 0|13| 2| 0|10| 0|18| 7| 0|15
%e A380154 ------------------------------------------------------------------
%e A380154 Day            15|16|17|18|19|20|21|22|23|24|25|26|27|28|29|30
%e A380154 Golden number   4| 0|12| 1| 0| 9| 0|17| 6| 0|14| 3| 0|11|19| 8
%e A380154 .
%e A380154 May
%e A380154 ------------------------------------------------------------------
%e A380154 Day            1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14
%e A380154 Golden number  0|16| 5| 0|13| 2| 0|10| 0|18| 7| 0|15| 4
%e A380154 ------------------------------------------------------------------
%e A380154 Day            15|16|17|18|19|20|21|22|23|24|25|26|27|28|29|30|31
%e A380154 Golden number   0|12| 1| 0| 9| 0|17| 6| 0|14| 3| 0|11|19| 0| 8| 0
%e A380154 .
%e A380154 June
%e A380154 ------------------------------------------------------------------
%e A380154 Day            1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14
%e A380154 Golden number 16| 5| 0|13| 2| 0|10| 0|18| 7| 0|15| 4| 0
%e A380154 ------------------------------------------------------------------
%e A380154 Day            15|16|17|18|19|20|21|22|23|24|25|26|27|28|29|30
%e A380154 Golden number  12| 1| 0| 9| 0|17| 6| 0|14| 3| 0|11|19| 8| 0|16
%e A380154 .
%e A380154 July
%e A380154 ------------------------------------------------------------------
%e A380154 Day            1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14
%e A380154 Golden number  5| 0|13| 2| 0|10| 0|18| 7| 0|15| 4| 0|12
%e A380154 ------------------------------------------------------------------
%e A380154 Day            15|16|17|18|19|20|21|22|23|24|25|26|27|28|29|30|31
%e A380154 Golden number   1| 0| 9| 0|17| 6| 0|14| 3| 0|11|19| 0| 8| 0|16| 5
%e A380154 .
%e A380154 August
%e A380154 ------------------------------------------------------------------
%e A380154 Day            1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14
%e A380154 Golden number  0|13| 2| 0|10| 0|18| 7| 0|15| 4| 0|12| 1
%e A380154 ------------------------------------------------------------------
%e A380154 Day            15|16|17|18|19|20|21|22|23|24|25|26|27|28|29|30|31
%e A380154 Golden number   0| 9| 0|17| 6| 0|14| 3| 0|11|19| 8| 0|16| 5| 0|13
%e A380154 .
%e A380154 September
%e A380154 ------------------------------------------------------------------
%e A380154 Day            1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14
%e A380154 Golden number  2| 0|10| 0|18| 7| 0|15| 4| 0|12| 1| 0| 9
%e A380154 ------------------------------------------------------------------
%e A380154 Day            15|16|17|18|19|20|21|22|23|24|25|26|27|28|29|30
%e A380154 Golden number   0|17| 6| 0|14| 3| 0|11|19| 0| 8| 0|16| 5| 0|13
%e A380154 .
%e A380154 October
%e A380154 ------------------------------------------------------------------
%e A380154 Day            1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14
%e A380154 Golden number  2| 0|10| 0|18| 7| 0|15| 4| 0|12| 1| 0| 9
%e A380154 ------------------------------------------------------------------
%e A380154 Day            15|16|17|18|19|20|21|22|23|24|25|26|27|28|29|30|31
%e A380154 Golden number   0|17| 6| 0|14| 3| 0|11|19| 8| 0|16| 5| 0|13| 2| 0
%e A380154 .
%e A380154 November
%e A380154 ------------------------------------------------------------------
%e A380154 Day            1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14
%e A380154 Golden number 10| 0|18| 7| 0|15| 4| 0|12| 1| 0| 9| 0|17
%e A380154 ------------------------------------------------------------------
%e A380154 Day            15|16|17|18|19|20|21|22|23|24|25|26|27|28|29|30
%e A380154 Golden number   6| 0|14| 3| 0|11|19| 0| 8| 0|16| 5| 0|13| 2| 0
%e A380154 .
%e A380154 December
%e A380154 ------------------------------------------------------------------
%e A380154 Day            1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14
%e A380154 Golden number 10| 0|18| 7| 0|15| 4| 0|12| 1| 0| 9| 0|17
%e A380154 ------------------------------------------------------------------
%e A380154 Day            15|16|17|18|19|20|21|22|23|24|25|26|27|28|29|30|31
%e A380154 Golden number   6| 0|14| 3| 0|11|19| 8| 0|16| 5| 0|13| 2| 0|10| 0
%e A380154 .
%e A380154 Full moons in 2025:
%e A380154 ((2025-5) mod 19) + 1 = 7.
%e A380154 This gives us the dates:
%e A380154   13. January, 12. February, 13. March,
%e A380154   12. April, 11. May, 10. June,
%e A380154   9. July, 8. August, 6. September,
%e A380154   6. October, 4. November, 4. December.
%o A380154 (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]}
%Y A380154 Cf. A057349, A098476, A131773, A348924, A349710.
%K A380154 nonn,fini
%O A380154 1,1
%A A380154 _Thomas Scheuerle_, Jan 13 2025

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.