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.

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

1,1

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

Table of n, a(n) for n=1..61.

Index entries for sequences related to calendars

Formula

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

Mathematica

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

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).

Sequence in context: A255774 A364005 A081838 * A067008 A376959 A189757

Adjacent sequences: A057344 A057345 A057346 * A057348 A057349 A057350

Keyword

nonn,easy

Author

Mitch Harris

Status

approved