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 1-4 of 4 results.

A057347 Leap years in the Islamic calendar starting year 1 AH (Anno Hegirae) = 622 CE (Common Era or AD). There are 11 leap years in a 30 year cycle.

Original entry on oeis.org

2, 5, 7, 10, 13, 16, 18, 21, 24, 26, 29, 32, 35, 37, 40, 43, 46, 48, 51, 54, 56, 59, 62, 65, 67, 70, 73, 76, 78, 81, 84, 86, 89, 92, 95, 97, 100, 103, 106, 108, 111, 114, 116, 119, 122, 125, 127, 130, 133, 136, 138, 141, 144, 146, 149, 152, 155, 157, 160, 163, 166
Offset: 1

Views

Author

Mitch Harris

Keywords

Comments

An Islamic year approximates 12 lunar months with 354 11/30 days (or 30 years with 10631 days).
Also, numbers m such that ((14 + 11*m) mod 30) < 11.
Worldwide, five different Islamic leap-year sequences are currently in use; this sequence (called "Fazari") is the most common of the five. See A350539. - Robert B Fowler, Dec 07 2022

References

  • N. Dershowitz and E. M. Reingold, Calendrical Calculations, Cambridge University Press, 1997.

Links

Crossrefs

Cf. A057349 (Hebrew calendar leap years).
Cf. A057348 (Islamic months lengths), A008685 (Gregorian months lengths),
Cf. A350539 (Islamic New Year JDN and 8 Islamic calendar variants).

Programs

  • Mathematica
    Select[Range[100], LeapYearQ[{#}, CalendarType -> "Islamic"]&] (* Jean-François Alcover, Apr 26 2020 *)

Formula

a(n) = floor((30*n - 4)/11).

A057348 Days in months in the Islamic calendar starting from Muharram, 1 AH. The twelfth month has 30 days in a leap year.

Original entry on oeis.org

30, 29, 30, 29, 30, 29, 30, 29, 30, 29, 30, 29, 30, 29, 30, 29, 30, 29, 30, 29, 30, 29, 30, 30, 30, 29, 30, 29, 30, 29, 30, 29, 30, 29, 30, 29, 30, 29, 30, 29, 30, 29, 30, 29, 30, 29, 30, 29, 30, 29, 30, 29, 30, 29, 30, 29, 30, 29, 30, 30, 30, 29, 30, 29, 30, 29, 30, 29, 30
Offset: 1

Views

Author

Mitch Harris

Keywords

Comments

The months' names are Muharram, Safar, Rabi I, Rabi II, Jumada I, Jumada II, Rajab, Shaban, Ramadan, Shawwal, Dhu al-Qada, Dhu al-Hijja. The year, 354 11/30 days long, is defined as 12 lunar months and so travels around the solar year.
Periodic with period 360; the average month length is 29 + 191/360 = 29.530555... days. This is about 0.000032425 days shorter than the synodic month. - Charles R Greathouse IV, Mar 28 2016
Worldwide, five different Islamic leap-year cycles are currently in use; the month lengths a(n) correspond to the most common leap-year sequence (called "Fazari"). See A350539. - Robert B Fowler, Dec 07 2022

References

  • N. Dershowitz and E. M. Reingold, Calendrical Calculations, Cambridge University Press, 1997.

Links

Crossrefs

Cf. A057347, A350539.

Programs

  • Maple
    isIslamicLeapYear := year -> irem(11 * year + 14, 30) < 11:
LastDayOfIslamicMonth := (year, month) -> if irem(month, 2) = 1 or (month = 12 and isIslamicLeapYear(year)) then 30 else 29 fi:
seq(seq(LastDayOfIslamicMonth(year, month), month=1..12), year = 1..5);
# Peter Luschny, Jan 07 2022
  • Mathematica
    If[Mod[n, 2]==1, 30, If[Mod[n, 12]!=0, 29, If[Mod[14+11(Floor[(n-1)/12]+1), 30]<11, 30, 29]]]
  • PARI
    a(n)=if(n%2,30,n%12,29,(n/12*11+14)%30<11,30,29) \\ Charles R Greathouse IV, Mar 28 2016

Formula

From Robert B Fowler, Dec 07 2022: (Start)
y = floor((n-1)/12) + 1 (Islamic year number)
m = ((n-1) mod 12) + 1 (Islamic month number)
a(n) = 29 + (m mod 2) + floor(m/12)*(floor((11*(y+1)+3)/30) - floor((11*y+3)/30)). (End)

A350471 The number of days elapsed since the Gregorian (proleptic) date Sunday, December 31, 1 BC on 1/1/n, where 1/1/n is the Gregorian date in the format month/day/year, the New Year's Day of the year n.

Original entry on oeis.org

1, 366, 731, 1096, 1462, 1827, 2192, 2557, 2923, 3288, 3653, 4018, 4384, 4749, 5114, 5479, 5845, 6210, 6575, 6940, 7306, 7671, 8036, 8401, 8767, 9132, 9497, 9862, 10228, 10593, 10958, 11323, 11689, 12054, 12419, 12784, 13150, 13515, 13880, 14245, 14611, 14976, 15341, 15706
Offset: 1

Views

Author

Peter Luschny, Jan 02 2022

Keywords

Comments

The number of days elapsed since the Gregorian date Sunday, December 31, 1 BC is also called the 'absolute date'. Note that there was no year 0. Thus this sequence shows the absolute date of the New Year's Day of the year n.

Examples

			Gregorian date 1/1/2022 = Julian date 12/19/2021 = Hebrew date 10/28/5782 = Islamic date 5/27/1443 = absolute date 738156.

Links

Crossrefs

Cf. A350458 (Hebrew Calendar), A350539 (Islamic Calendar).

Programs

  • Python
    def A350471(n):
    m = n - 1
    return 1 + 365 * m + m // 4 - m // 100 + m // 400
print([A350471(n) for n in range(1, 45)])

Formula

From Robert B Fowler, Aug 20 2024: (Start)
a(n) = 1 + 365*m + floor(m/4) - floor(m/100) + floor(m/400), where m = n-1.
a(n+400*k) = a(n) + 146097*k. (End)

A097105 Gregorian years containing two Islamic New Year Days.

Original entry on oeis.org

640, 672, 705, 738, 770, 803, 835, 868, 900, 933, 966, 998, 1031, 1063, 1096, 1129, 1161, 1194, 1226, 1259, 1291, 1324, 1357, 1389, 1422, 1454, 1487, 1520, 1552, 1585, 1617, 1650, 1682, 1715, 1748, 1780, 1813, 1845, 1878, 1911, 1943, 1976, 2008, 2041
Offset: 1

Views

Author

Leonid Broukhis, Sep 15 2004

Keywords

Comments

Gregorian years containing "blue" Islamic New Year Days. The boundary of a calendrical period is hereby called "blue" w.r.t. a similarly named period in another calendar when the shorter one does not contain the boundaries of the longer one. Gregorian calendar prior to 1582 is proleptic, extrapolated according to the calculator in the links.
The ratio of Gregorian to Islamic Year is 365.2425/354.36666... = 438291/425240. The interesting approximating continuous fractions are 403/391, 638/619, 1041/1010 and a very long sequence of (1041+403*n)/(1010+391*n), ending with 7489/7266, so the 403/391 pattern will remain for thousands of years.
Because 4382910 Islamic years = 1553157207 days = 4252400 Gregorian years, each cycle contains 130510 blue Gregorian years and therefore a(n + 130510*k) = a(n) + 425400*k for k >= 0. - Robert B Fowler, Dec 06 2022
Note that the unique "crosspoint" year of the two calendars (20874) is also a blue year, with the first Islamic New Year falling on January 3, i.e., 01/01/20874 (Islamic) = 01/03/20874 (Gregorian). - Robert B Fowler, Dec 06 2022

Examples

			1396-1-1 A.H. = 1976-01-03 C.E.
1397-1-1 A.H. = 1976-12-23 C.E. therefore 1976 is listed. (Corrected by _Robert B Fowler_, Mar 03 2022)

Links

  • John Walker, Calendar Converter (Warning: as of 12/7/2022, the first leap years in the 30-year Islamic cycle are listed as 1, 5, 7, ..., but are actually 2, 5, 7, ...; the calendar calculations, however, are correct. - _Robert B Fowler_, Dec 08 2022)

Crossrefs

Cf. A350539.

Formula

I(i) = chronological Julian Day Number (JDN) of New Year day of Islamic year i
= 1948086 + floor((10631*i+3)/30) (see A350539)
G(g) = JDN of New Year day of Gregorian year g+1 (not year g)
= 1721426 + floor(1461*g/4) - floor(g/100) + floor(g/400)
initialize values: i=1, g=621, n=0
repeat forever:
increment: i = i+1, g = g+1
IF I(i) < G(g) THEN n = n+1, a(n) = g, i = i+1 - Robert B Fowler, Dec 06 2022

Extensions

New name by Robert B Fowler, Mar 03 2022
Showing 1-4 of 4 results.

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