A320467 Two-column table read by rows: The Mayan 260-day Tzolkin cycle, with day names replaced by numbers.

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

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(2n-1) = ((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[(n-1)/2, 13] + 1)*Mod[n, 2]+(Mod[n/2-1, 20] + 1)*(1-Mod[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