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

Author

Mitch Harris

Keywords

• nonn
• easy

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

• Index entries for sequences related to calendars

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).