A057347 - OEIS

%I #22 Dec 08 2022 16:43:07

%S 2,5,7,10,13,16,18,21,24,26,29,32,35,37,40,43,46,48,51,54,56,59,62,65,

%T 67,70,73,76,78,81,84,86,89,92,95,97,100,103,106,108,111,114,116,119,

%U 122,125,127,130,133,136,138,141,144,146,149,152,155,157,160,163,166

%N 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.

%C An Islamic year approximates 12 lunar months with 354 11/30 days (or 30 years with 10631 days).

%C Also, numbers m such that ((14 + 11*m) mod 30) < 11.

%C 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

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

%H <a href="/index/Ca#calendar">Index entries for sequences related to calendars</a>

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

%t Select[Range[100], LeapYearQ[{#}, CalendarType -> "Islamic"]&] (* _Jean-François Alcover_, Apr 26 2020 *)

%Y Cf. A057349 (Hebrew calendar leap years).

%Y Cf. A057348 (Islamic months lengths), A008685 (Gregorian months lengths),

%Y Cf. A350539 (Islamic New Year JDN and 8 Islamic calendar variants).

%K nonn,easy

%O 1,1

%A _Mitch Harris_