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

Author

Lucian Craciun, Oct 13 2018

Keywords

• easy
• fini
• full
• nonn
• tabf

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A081244, A215146.

Programs

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 *)

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