login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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