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A057349 Leap years in the Hebrew Calendar starting in year 1 (3761 BCE). The leap year has an extra-month. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

REFERENCES

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

LINKS

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

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).

FORMULA

a(n) = floor((19*n + 5)/7).

a(n) = A083033(n) + n + 2. - Ralf Stephan, Feb 24 2004

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

MATHEMATICA

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 *)

PROG

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

CROSSREFS

Cf. A008685, Hebrew month pattern A057350, A057347.

Cf. A350458 (JDN of Tishri 1 each year starting with year 1).

Sequence in context: A198084 A047399 A342744 * A087068 A022851 A325946

Adjacent sequences: A057346 A057347 A057348 * A057350 A057351 A057352

KEYWORD

nonn,easy

AUTHOR

Mitch Harris

STATUS

approved

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Last modified December 3 23:46 EST 2022. Contains 358544 sequences. (Running on oeis4.)