

A102241


Hexagrams of the Yi Jing [or I Ching] interpreted in base 10, with the top line = 2^5 (most significant bit) and the bottom line as 2^0 (least significant bit).


2



63, 0, 17, 34, 23, 58, 2, 16, 55, 59, 7, 56, 61, 47, 4, 8, 25, 38, 3, 48, 41, 37, 32, 1, 57, 39, 33, 30, 18, 45, 28, 14, 60, 15, 40, 5, 53, 43, 20, 10, 35, 49, 31, 62, 24, 6, 26, 22, 29, 46, 9, 36, 52, 11, 13, 44, 54, 27, 50, 19, 51, 12, 21, 42
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OFFSET

1,1


COMMENTS

Traditionalists insist that the hexagrams were built from trigrams, which were in turn built from single lines. Historians point out that this is not supported by facts, the hexagrams came first and the rest has evolved from commentary.
There are at least 5 orderings: The popular book order (known as the WenWan ordering, this sequence), the MaWangDui order (A125638), the LianShan ordering (partial), the KueiTsan ordering (partial) and the most recent binary ordering, known as the FuHsi ordering (probably by Shao Yung, +1000 most certainly influenced by Yang Hsiung's Tai Hsuan Jing +10).
In a similar vein the TaiHsuan Jing (Han Dynasty, Yang TzeYun or Yang Hsiung about +10). This book uses four layers of unbroken, broken once and twicebroken lines that result in the numbers 00  80 arranged in a basethree number system order. This book may have also influenced Leibniz.
To my knowledge the orderings of the hexagrams have not been explained mathematically (apart from the obvious fact that each hexagram is followed by its binary reversal or binary complement if it is a binary palindrome).


REFERENCES

D. E. Knuth, The Art of Computer Programming, vol. 4A, Combinatorial Algorithms, Section 7.2.1.7 (p. 486).
Unknown author, Yi Jing (also known as the Chou Yi). Translation by Richard Wilhelm (Chinese to German) and Cary F. Baynes (German to English).
Unknown author, Yi Jing, English Translation of the MaWangDui text (which has a different ordering).


LINKS

Table of n, a(n) for n=1..64.
Andreas Schoeter, Yi Jing Algebra
Greg Whincup, The I Ching on the Net
Wikipedia, I Ching


EXAMPLE

The original hexagrams (in binary) are 111111, 000000, 010001, 100010, 010111, 111010, 000010, 010000, 110111, 111011, 000111, 111000, 111101, 101111, 000100, 001000, 011001, 100110, 000011, 110000, 101001, 100101, 100000, 000001, 111001, 100111, 100001, 011110, 010010, 101101, 011100, 001110, 111100, 001111, 101000, 000101, 110101, 101011, 010100, 001010, 100011, 110001, 011111, 111110, 011000, 000110, 011010, 010110, 011101, 101110, 001001, 100100, 110100, 001011, 001101, 101100, 110110, 011011, 110010, 010011, 110011, 001100, 010101, 101010.


CROSSREFS

Cf. A125638.
Sequence in context: A159374 A115460 A116270 * A255915 A234692 A084507
Adjacent sequences: A102238 A102239 A102240 * A102242 A102243 A102244


KEYWORD

nonn,fini,full


AUTHOR

Patrick A. Kirol [Sun Wu Kong] (sunwukong(AT)hananet.net), Feb 18 2005, Nov 28 2008


EXTENSIONS

Corrected by David Applegate, Nov 28 2006


STATUS

approved



