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.
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
Examples
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.
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.
- Index entries for sequences related to final digits of numbers
Programs
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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 *)
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
Comments