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 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. 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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) REFERENCES 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." LINKS 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. FORMULA 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 EXAMPLE 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. MATHEMATICA 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 *) CROSSREFS Cf. A060582, A270740. Sequence in context: A318702 A226519 A066057 * A221167 A286134 A276469 Adjacent sequences:  A060585 A060586 A060587 * A060589 A060590 A060591 KEYWORD base,nonn AUTHOR Henry Bottomley, Apr 04 2001 STATUS approved

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Last modified April 3 20:26 EDT 2020. Contains 333199 sequences. (Running on oeis4.)