A060582 -id:A060582 - cp's OEIS frontend

A060583 A ternary code related to the Tower of Hanoi.

0, 2, 1, 7, 6, 8, 5, 4, 3, 23, 22, 21, 18, 20, 19, 25, 24, 26, 16, 15, 17, 14, 13, 12, 9, 11, 10, 70, 69, 71, 68, 67, 66, 63, 65, 64, 54, 56, 55, 61, 60, 62, 59, 58, 57, 77, 76, 75, 72, 74, 73, 79, 78, 80, 50, 49, 48, 45, 47, 46, 52, 51, 53, 43, 42, 44, 41, 40, 39, 36, 38, 37

Offset: 0

Henry Bottomley, Apr 04 2001

Write n in base 3, then (working from left to right) if the k-th digit of n is equal to the corresponding digit to the left of the k-th digit of a(n) then this is the k-th digit of a(n), otherwise the k-th digit of a(n) is the element of {0,1,2} which has not just been compared, then read result as a base 3 number.

			a(46) = 76 since 43 = 1201_3; this gives a first digit of 2(=3-1-0), a second digit of 2(=2=2), a third digit of 1(=3-2-0) and a fourth digit of 1(=1=1); 2211_3 = 76.

Cf. A060586, A060587 (inverse).

a(n) = 3*a(floor(n/3)) + ((-a(floor(n/3))-n) mod 3) = 3*a(floor(n/3)) + A060582(n) with a(0)=0.

A060588 If the final two digits of n written in base 3 are the same then this digit, otherwise mod 3-sum of these two digits.

Original entry on oeis.org

0, 2, 1, 2, 1, 0, 1, 0, 2, 0, 2, 1, 2, 1, 0, 1, 0, 2, 0, 2, 1, 2, 1, 0, 1, 0, 2, 0, 2, 1, 2, 1, 0, 1, 0, 2, 0, 2, 1, 2, 1, 0, 1, 0, 2, 0, 2, 1, 2, 1, 0, 1, 0, 2, 0, 2, 1, 2, 1, 0, 1, 0, 2, 0, 2, 1, 2, 1, 0, 1, 0, 2, 0, 2, 1, 2, 1, 0, 1, 0, 2, 0, 2, 1, 2, 1, 0, 1, 0, 2, 0, 2, 1, 2, 1, 0, 1, 0, 2, 0, 2, 1, 2, 1, 0

Offset: 0

Henry Bottomley, Apr 04 2001

From William Walkington, Sep 14 2016: (Start)
With offset 1, the y-coordinates of position vectors from the origin (point 1) to the points numbered 1 to N^2 of the magic tori that display the Agrippa odd-order-N magic squares can be expressed as follows: a(n) = (-(n-1)-floor((n-1)/N)) mod N.
This generates the y-coordinates of the magic tori that display the Agrippa order-3 "Saturn," order-5 "Mars," order-7 "Venus," order-9 "Luna," and higher-odd-order-N magic squares.
Therefore, if the odd-order-N of the torus is 3, then the resulting sequence 0,2,1,2,1,0,1,0,2 represents the y-coordinates of position vectors from the origin (point number 1) to the point numbered 1 to 9 of the magic torus that displays the Agrippa order-3 "Saturn" magic square. (End)

			a(22)=1 since 22 is written in base 3 as 211 and the final two digits are 1; a(23)=0 since 23 is written in base 3 as 212 and the final two digits are 1 and 2 and 3-(1+2)=0.

H.C. Agrippa, "De occulta philosophia Libri tres," (1533) translated by "J.F." (John French?) and printed by Moule, London, in 1651, Book II, chapter XXII entitled "Of the tables of the Planets, their vertues,forms, and what Divine names, Intelligencies, and Spirits are set over them."

H. C. Agrippa, De Occulta Philosophia libri tres (Three books of occult philosophy), Book II, chapter XXII, Digital edition Peterson J.F.
W. Walkington, Magic torus coordinate and vector symmetries.
William Walkington, Agrippa odd-order magic squares
Wikipedia, Agrippa's magic squares.
Index entries for sequences related to final digits of numbers

Cf. A060582, A270740.

b3d[n_]:=Module[{d3=Take[IntegerDigits[n,3],-2]},If[MatchQ[d3,{x_, x_}], d3[[1]],3-Total[d3]]]; Join[{0,2,1},Array[b3d,110,3]] (* Harvey P. Dale, Feb 29 2016 *)
Table[If[MatchQ @@ #, First@ #, Mod[3 - Total@ #, 3]] &@ Take[PadLeft[#, 2], -2] &@ IntegerDigits[n, 3], {n, 0, 120}] (* or *)
Table[Mod[-n - Floor[n/3], 3], {n, 0, 120}] (* Michael De Vlieger, Sep 14 2016 *)

a(n) = a(n-9) = (-[n/3]-n) mod 3 = A060587(n) mod 3.

a(n) = (-n - floor(n/3)) mod 3. - William Walkington, Sep 14 2016

cp's OEIS Frontend

A060583 A ternary code related to the Tower of Hanoi.

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