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 A292779 Interpret the values of the Moebius function mu(k) for k = n to 1 as a balanced ternary number. 3
 1, -2, -11, -11, -92, 151, -578, -578, -578, 19105, -39944, -39944, -571385, 1022938, 5805907, 5805907, -37240814, -37240814, -424661303, -424661303, 3062123098, 13522476301, -17858583308, -17858583308, -17858583308, 829430026135, 829430026135, 829430026135 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Balanced ternary is much like regular ternary, but with the crucial difference of using the digit -1 instead of the digit 2. Then some powers of 3 are added, others are subtracted. Since the least significant digit is always 1, a(n) is never a multiple of 3. If mu(n) = 0, then a(n) is the same as a(n - 1). Run lengths are given by A076259. - Andrey Zabolotskiy, Oct 13 2017 LINKS Seiichi Manyama, Table of n, a(n) for n = 1..1000 Wikipedia, Balanced ternary FORMULA a(n) = Sum_{k = 1 .. n} mu(k) 3^(k - 1). EXAMPLE mu(1) = 1, so a(1) = 1 * 3^0 = 1. mu(2) = -1, so a(2) = -1 * 3^1 + 1 * 3^0 = -3 + 1 = -2. mu(3) = -1, so a(3) = -1 * 3^2 + -1 * 3^1 + 1 * 3^0 = -9 - 3 + 1 = -11. mu(4) = 0, so a(4) = 0 * 3^3 + -1 * 3^2 + -1 * 3^1 + 1 * 3^0 = -9 - 3 + 1 = -11. MAPLE a:= proc(n) option remember; `if`(n=0, 0,       a(n-1)+3^(n-1)*numtheory[mobius](n))     end: seq(a(n), n=1..33);  # Alois P. Heinz, Oct 13 2017 MATHEMATICA Table[3^Range[0, n - 1].MoebiusMu[Range[n]], {n, 50}] PROG (PARI) a(n) = sum(k=1, n, moebius(k)*3^(k-1)); \\ Michel Marcus, Oct 01 2017 CROSSREFS Cf. A008683, A127513, A292524. Sequence in context: A265545 A153705 A290394 * A245521 A275617 A090009 Adjacent sequences:  A292776 A292777 A292778 * A292780 A292781 A292782 KEYWORD easy,sign,base AUTHOR Alonso del Arte, Sep 22 2017 STATUS approved

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Last modified June 14 21:27 EDT 2021. Contains 345041 sequences. (Running on oeis4.)