

A320467


Twocolumn table read by rows: The Mayan 260day Tzolkin cycle, with day names replaced by numbers.


1



1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 1, 14, 2, 15, 3, 16, 4, 17, 5, 18, 6, 19, 7, 20, 8, 1, 9, 2, 10, 3, 11, 4, 12, 5, 13, 6, 1, 7, 2, 8, 3, 9, 4, 10, 5, 11, 6, 12, 7, 13, 8, 14, 9, 15, 10, 16, 11, 17, 12, 18
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OFFSET

1,3


COMMENTS

Day 1 of year 1 of the Mayan Long Count calendar (0.0.1.0.1) coincides with the first day of the Tzolkin cycle (1,1). Two Tzolkin cycles before that date, there was a new moon.


LINKS

Lucian Craciun, Table of n, a(n) for n = 1..520
John Walker, Calendar Converter.
Wikipedia, Tzolk'in.
Wikipedia, Mesoamerican Long Count calendar.


FORMULA

a(2n1) = ((n  1) mod 13) + 1.
a(2n) = ((n  1) mod 20) + 1.
a(n) = ((n  1)/2 mod 13 + 1)*(n mod 2) + ((n/2  1) mod 20 + 1)*(1  (n mod 2)).  Stefano Spezia, Dec 07 2018


EXAMPLE

The first pair, (1,1), represents 1 Imix; the second pair, (2,2), represents 2 Ik; the thirteenth pair, (13,13), represents 13 Ben; the fourteenth pair, (1,14), represents 1 Ix; the fifteenth pair, (2,15), represents 2 Men; etc.


MATHEMATICA

For[{A := {}, k := 0}, k < 260, k++, A = Append[A, {1 + Mod[k, 13], 1 + Mod[k, 20]}]]; Flatten[A]
a[n_]:=(Mod[(n1)/2, 13] + 1)*Mod[n, 2]+(Mod[n/21, 20] + 1)*(1Mod[n, 2]); Array[a, 260] (* Stefano Spezia, Dec 07 2018 *)


CROSSREFS

Cf. A081244, A215146.
Sequence in context: A135020 A242681 A034888 * A086388 A111660 A244325
Adjacent sequences: A320464 A320465 A320466 * A320468 A320469 A320470


KEYWORD

easy,fini,full,nonn,tabf


AUTHOR

Lucian Craciun, Oct 13 2018


STATUS

approved



