A350458 -id:A350458 - cp's OEIS frontend

A057349 Leap years in the Hebrew Calendar starting in year 1 (3761 BCE). The leap year has an extra month.

3, 6, 8, 11, 14, 17, 19, 22, 25, 27, 30, 33, 36, 38, 41, 44, 46, 49, 52, 55, 57, 60, 63, 65, 68, 71, 74, 76, 79, 82, 84, 87, 90, 93, 95, 98, 101, 103, 106, 109, 112, 114, 117, 120, 122, 125, 128, 131, 133, 136, 139, 141, 144, 147, 150, 152, 155, 158, 160, 163, 166

Offset: 1

Mitch Harris

A Hebrew year approximates a solar year with 12 and 7/19 lunar months (or 19 years with 235 months, the 19-year Metonic cycle).
Also numbers m such that (1 + 7*m) mod 19 < 7.
In equal musical temperament, when an octave is divided into twelve half steps (a half step involves two notes and a whole step involves three notes, giving a total of thirteen notes including the octave), whole (w) and half (h) step intervals of the major scale follow a pattern of 2w-1h-3w-1h. Assigning the integer 2 (notes) to the half-step and 3 (notes) to the whole-step intervals will result in the same sequence when applied to the major scale. - Gergely Földvári, Jul 28 2024

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

Gergely Földvári, Illustration of the correlation between leap years of the Hebrew calendar and the musical major scale
Robinson Meyer, The Ancient Math That Sets the Date of Easter and Passover: Why don't the two holidays always coincide?, The Atlantic, April 19, 2019.
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,1,-1).

Cf. A008685, Hebrew month pattern A057350, A057347.
Cf. A350458 (JDN of Tishri 1 each year starting with year 1).
Cf. A083033 (Dorian musical scale), A083089 (Lydian musical scale).

LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, -1}, {3, 6, 8, 11, 14, 17, 19, 22}, 70] (* Harvey P. Dale, Jan 18 2015 *)
Floor[(19Range[70] + 5)/7] (* Alonso del Arte, Apr 21 2019 *)

a(n)=(19*n+5)\7 \\ Charles R Greathouse IV, Dec 07 2011

a(n) = floor((19*n + 5)/7).
a(n) = A083033(n) + n + 2. - Ralf Stephan, Feb 24 2004
a(n) = A083089(n+1) + n. - Robert B Fowler, Dec 07 2022
G.f.: x*(2*x^6 + 3*x^5 + 3*x^4 + 3*x^3 + 2*x^2 + 3*x + 3)/((x - 1)^2*(x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)). - Colin Barker, Jul 02 2012

A057350 Days in months in the Hebrew calendar starting from Nisan 5760 (Spring 2000 CE).

Original entry on oeis.org

30, 29, 30, 29, 30, 29, 30, 30, 30, 29, 30, 30, 29, 30, 29, 30, 29, 30, 29, 30, 29, 29, 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, 30, 29, 30, 29, 30, 29, 30, 29, 30, 30, 30, 29, 30, 29, 30, 29, 30, 29, 30, 29, 30, 29, 29, 29, 30, 30, 29

Offset: 0

Mitch Harris

The months are Nisan, Iyyar, Sivan, Tammuz, Av, Elul, Tishri, Heshvan, Kislev, Teveth, Shevat, Adar. A leap month of 30 days, added between Shevat and Adar, is called Adar I, where the final month is then called Adar II. Heshvan and Kislev (the 8th and 9th months) may each have 29 or 30 days, depending on the calendrical rules.
36.22% of all years are "regular"; 25.51% are "deficient", with 29 days in both Heshvan and Kislev; 38.27% are "complete", with 30 days in both months. Note that Hebrew year 5760 is a 13-month leap year. - Robert B Fowler, Mar 08 2022
See A350458 for other comments, references, links, formulas, programs.

			A regular year has the pattern 30, 29, 30, 29, 30, 29, 30, 29, 30, 29, 30, 29.

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

Wikipedia, Hebrew calendar Four gates, Types of Hebrew calendar years and their frequencies.

Cf. A057349 (Hebrew leap years).

Cf. A350458 (Chronological JDN of Tishri 1 in Hebrew calendar year (AM) n).

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

Peter Luschny, Jan 02 2022

nonn

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.

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

Peter Luschny, Table of n, a(n) for n = 1..3000
Peter Luschny, Calendars, Conversions of Dates, Change of Calendars, GitHub 2022.
John Walker, Calendar Converter.
Wikipedia, Gregorian calendar.
Index entries for sequences related to calendars

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

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)])

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)

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A057349 Leap years in the Hebrew Calendar starting in year 1 (3761 BCE). The leap year has an extra month.

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A057350 Days in months in the Hebrew calendar starting from Nisan 5760 (Spring 2000 CE).

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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.

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