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
KEYWORD
easy,fini,full,nonn,tabf
AUTHOR
Lucian Craciun, Oct 13 2018
STATUS
approved