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%I #21 May 19 2021 10:22:32
%S 1,-2,-11,-11,-92,151,-578,-578,-578,19105,-39944,-39944,-571385,
%T 1022938,5805907,5805907,-37240814,-37240814,-424661303,-424661303,
%U 3062123098,13522476301,-17858583308,-17858583308,-17858583308,829430026135,829430026135,829430026135
%N Interpret the values of the Moebius function mu(k) for k = n to 1 as a balanced ternary number.
%C 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.
%C Since the least significant digit is always 1, a(n) is never a multiple of 3.
%C If mu(n) = 0, then a(n) is the same as a(n - 1).
%C Run lengths are given by A076259. - _Andrey Zabolotskiy_, Oct 13 2017
%H Seiichi Manyama, <a href="/A292779/b292779.txt">Table of n, a(n) for n = 1..1000</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Balanced_ternary">Balanced ternary</a>
%F a(n) = Sum_{k = 1 .. n} mu(k) 3^(k - 1).
%e mu(1) = 1, so a(1) = 1 * 3^0 = 1.
%e mu(2) = -1, so a(2) = -1 * 3^1 + 1 * 3^0 = -3 + 1 = -2.
%e mu(3) = -1, so a(3) = -1 * 3^2 + -1 * 3^1 + 1 * 3^0 = -9 - 3 + 1 = -11.
%e mu(4) = 0, so a(4) = 0 * 3^3 + -1 * 3^2 + -1 * 3^1 + 1 * 3^0 = -9 - 3 + 1 = -11.
%p a:= proc(n) option remember; `if`(n=0, 0,
%p a(n-1)+3^(n-1)*numtheory[mobius](n))
%p end:
%p seq(a(n), n=1..33); # _Alois P. Heinz_, Oct 13 2017
%t Table[3^Range[0, n - 1].MoebiusMu[Range[n]], {n, 50}]
%o (PARI) a(n) = sum(k=1, n, moebius(k)*3^(k-1)); \\ _Michel Marcus_, Oct 01 2017
%Y Cf. A008683, A127513, A292524.
%K easy,sign,base
%O 1,2
%A _Alonso del Arte_, Sep 22 2017
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