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A057348
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Days in months in the Islamic calendar starting from Muharram, 1 AH. The twelfth month has 30 days in a leap year.
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5
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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
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OFFSET
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1,1
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COMMENTS
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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
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REFERENCES
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N. Dershowitz and E. M. Reingold, Calendrical Calculations, Cambridge University Press, 1997.
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LINKS
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FORMULA
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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)
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MAPLE
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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);
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MATHEMATICA
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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]]]
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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