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A320467 Two-column table read by rows: The Mayan 260-day 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 26 07:25 EST 2020. Contains 338632 sequences. (Running on oeis4.)