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 A292524 Interpret the values of the Moebius function mu(k) for k = 1 to n as a balanced ternary number. 2
 0, 1, 2, 5, 15, 44, 133, 398, 1194, 3582, 10747, 32240, 96720, 290159, 870478, 2611435, 7834305, 23502914, 70508742, 211526225, 634578675, 1903736026, 5711208079, 17133624236, 51400872708, 154202618124, 462607854373, 1387823563119, 4163470689357 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 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. If mu(n) = 0, then a(n) is a multiple of 3, specifically, it is thrice a(n - 1). Otherwise, a(n) is not a multiple of 3. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..2097 Wikipedia, Balanced ternary FORMULA a(n) = Sum_{k = 1..n} mu(k) 3^(n - k). 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 = 5. mu(4) = 0, so a(4) = 1 * 3^3 + -1 * 3^2 + -1 * 3^1 + 0 * 3^0 = 27 - 9 - 3 + 0 = 15. MAPLE a:= proc(n) option remember; `if`(n=0, 0,       a(n-1)*3+numtheory[mobius](n))     end: seq(a(n), n=0..33);  # Alois P. Heinz, Oct 13 2017 MATHEMATICA Table[Plus@@(3^Range[n - 1, 0, -1] MoebiusMu[Range[n]]), {n, 50}] PROG (PARI) a(n) = sum(k=1, n, moebius(k)*3^(n-k)); \\ Michel Marcus, Oct 01 2017 CROSSREFS Cf. A008683, A292779. Sequence in context: A094176 A084086 A307259 * A071742 A035355 A220873 Adjacent sequences:  A292521 A292522 A292523 * A292525 A292526 A292527 KEYWORD nonn,easy,base AUTHOR Alonso del Arte, Sep 18 2017 EXTENSIONS a(0)=0 prepended by Alois P. Heinz, Oct 13 2017 STATUS approved

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Last modified September 26 20:36 EDT 2020. Contains 337374 sequences. (Running on oeis4.)