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A115100 Mayan calendar periods in days. 1
1, 20, 360, 7200, 144000, 1872000 (list; graph; refs; listen; history; text; internal format)



"Mayan primes" may be defined as these periods plus or minus 1, namely: 2, 19, 359, 143999, 1872001. Note also that 361 = 19^2; 144001 = 11 * 13 * 19 * 53.

From the Hermetic Systems" link: "The Mayas used three different calendrical systems (and some variations within the systems). The three systems are known as the tzolkin (the sacred calendar), the haab (the civil calendar) and the long count system. The tzolkin is a cycle of 260 days and the haab is a cycle of 365 days (these cycles are explained in Sections 2 and 3 of this chapter). The tzolkin cycle and the haab cycle were combined to produce a cycle of 18,980 days, known as the calendar round. 18,980 days is a little less than 52 solar years.

"Thus the Mayas could not simply use a tzolkin/haab date to identify a day within a period of several hundred years because there would be several days within this period with the same tzolkin/haab date. The Mayas overcame this problem by using a third dating system which enabled them to identify a day uniquely within a period of 1,872,000 days (approximately 5,125.36 solar years).

"To do this they used a vigesimal (i.e. based on 20) place-value number system, analogous to our decimal place-value number system. The Mayas used a pure vigesimal system for counting objects but modified this when counting days."


Bourgeois, Julia F., The True Calendar-Years of Aztecs and Mayas and the True Mayan Calendar System, Editorial Cultura, Mexico, 1942.

Bowditch, C. P., The Numeration, Calendar Systems and Astronomical Knowledge of the Mayas, Cambridge University Press, 1910.

Brunhouse, R. L., Sylvanus G. Morley and the World of the Ancient Mayas, University of Oklahoma Press, 1971.


Table of n, a(n) for n=1..6.

Hermetic Systems: Maya and European Dates.

Index entries for sequences related to calendars


1 kin = 1 day.

1 uinal = 20 kins = 20 days.

1 tun = 18 uinals = 360 days.

1 katun = 20 tuns = 7200 days.

1 baktun = 20 katuns = 144000 days.

13 baktuns = 1 great cycle or Maya era = 1872000 days (approximately 5125.37 solar years).


Cf. A008684, A008685, A011763, A011770, A011771.

Fortnight related: A001356, A051121.

Related to names of months: A031139.

A subsequence of A081244.

Sequence in context: A004292 A053508 A060918 * A049683 A228330 A014901

Adjacent sequences:  A115097 A115098 A115099 * A115101 A115102 A115103




Jonathan Vos Post, Mar 02 2006


Edited by M. F. Hasler, Dec 23 2012



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Last modified February 27 10:09 EST 2021. Contains 341649 sequences. (Running on oeis4.)