A215879 Written in base 3, n ends in a(n) consecutive nonzero digits.

0, 1, 1, 0, 2, 2, 0, 2, 2, 0, 1, 1, 0, 3, 3, 0, 3, 3, 0, 1, 1, 0, 3, 3, 0, 3, 3, 0, 1, 1, 0, 2, 2, 0, 2, 2, 0, 1, 1, 0, 4, 4, 0, 4, 4, 0, 1, 1, 0, 4, 4, 0, 4, 4, 0, 1, 1, 0, 2, 2, 0, 2, 2, 0, 1, 1, 0, 4, 4, 0, 4, 4, 0, 1, 1, 0, 4, 4, 0, 4, 4, 0, 1, 1, 0, 2, 2, 0, 2, 2, 0, 1, 1, 0, 3, 3, 0, 3, 3, 0, 1, 1, 0, 3, 3, 0, 3

Offset

0,5

Comments

Somehow complementary to A007949, the 3-adic valuation of n.

The base 2 analog of this sequence essentially coincides with the 2-adic valuation A007814 (up to a shift in the index).

One gets back the same sequence by concatenation of the pattern (0,1,1) successively multiplied by a(n)+1 = 1, 2, 2, 1, 3, 3, ... for n = 0, 1, 2, 3, 4, 5, .... This is equivalent to the formula (a(n)+1)*(0, 1, 1) = a(3n, 3n+1, 3n+2). - M. F. Hasler, Aug 26 2012, corrected Aug 23 2022

a(A008585(n)) = 0; a(A001651(n)) > 0. - Reinhard Zumkeller, Dec 28 2012

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Formula

a(3^(t+1)*k+m) = t for 3^t > m > 3^(t-1).

a(3n) = 0, a(3n+1) = a(3n+2) = a(n)+1. - M. F. Hasler, Aug 26 2012, corrected thanks to a remark from Jianing Song, Aug 23 2022

Example

The numbers 0, 1, 2, 3, 4, 5, 6, 7 are written in base 3 as 0, 1, 2, 10, 11, 12, 20, 21 and thus end in a(0..7) = 0, 1, 1, 0, 2, 2, 0, 2 nonzero digits.

Mathematica

cnzd[n_]:=Module[{idn3=IntegerDigits[n, 3], len}, len=Length[idn3]; Which[ idn3[[len]] == 0, 0, Position[idn3, 0]=={}, len, True, len-Position[idn3, 0] [[-1, 1]]]]; Array[cnzd, 110, 0] (* Harvey P. Dale, Jun 07 2016 *)

Prog

(PARI) A215879(n, b=3)=n=divrem(n, b); for(c=0, oo, n[2]||return(c); n=divrem(n[1], b))
(PARI) a(n)=my(k); while(n%3, n\=3; k++); k \\ Charles R Greathouse IV, Sep 26 2013
(Haskell)
a215879 n = if t == 0 then 0 else a215879 n' + 1
            where (n', t) = divMod n 3
-- Reinhard Zumkeller, Dec 28 2012
(Python)
def A215879(n):
    c = 0
    while (a:=divmod(n, 3))[1]:
        c += 1
        n = a[0]
    return c # Chai Wah Wu, Oct 15 2022

Crossrefs

The base-4, base-5 and base-10 analogs of this sequence are given in A215883, A215884 and A215887.

Cf. A007089.

Sequence in context: A352557 A229723 A258040 * A114700 A353768 A140666

Adjacent sequences: A215876 A215877 A215878 * A215880 A215881 A215882

Keyword

nonn,base,nice

Author

M. F. Hasler, Aug 25 2012

Status

approved