A193879 Different leap years in the Gregorian and the revised Julian calendars

0, 2, 4, 6, 8, 11, 12, 15, 16, 28, 29, 32, 33, 36, 38, 40, 42, 44, 47, 48, 51, 52, 64, 65, 68, 69, 72, 74, 76, 78, 80, 83, 84, 87, 88, 100, 101, 104, 105, 108, 110, 112, 114, 116, 119, 120, 123, 124, 136, 137, 140, 141, 144, 146, 148, 150, 152, 155, 156, 159, 160

Offset

1,2

Comments

Terms divided by 100, e.g., 28 indicates year 2800, which is a Gregorian leap year, but not a revised Julian leap year. Values below 28 are "proleptic" (only based on the formula).

Links

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

M. Milankovitch, Das Ende des julianischen Kalenders und der neue Kalender der orientalischen Kirchen, Astronomische Nachrichten, volume 220 (1924), pages 379-384.

Claus Tøndering, Frequently Asked Questions about Calendars, Don't the Greeks do it differently?

Wikipedia, Revised Julian calendar

Formula

( N // 9 = 2 | N // 9 = 6 ) <> ( N // 4 = 0 )

Example

28 mod 9 is not 2 or 6, but 28 mod 4 is 0: 2800 is a Gregorian leap year.
29 mod 9 is 2, but 29 mod 4 is not 0: 2900 is a revised Julian leap year.

Crossrefs

A008586 enumerates "Gregorian leap centuries" (N // 4 = 0).

A193910 enumerates "revised Julian leap centuries".

Sequence in context: A073140 A256342 A171820 * A226722 A187414 A187348

Adjacent sequences: A193876 A193877 A193878 * A193880 A193881 A193882

Keyword

nonn,easy

Author

Frank Ellermann, Aug 07 2011

Status

approved