A122586 Leading digit of n expressed in base 3.

1, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

1,2

Comments

Values 1 and 2 appear alternately and each time in runs whose lengths are the powers of 3. Each power of 3 is used twice: once for a run of 1's and then for a run of 2's.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = floor(n/(3^floor(log(n)/log(3)))).

From Robert Israel, Mar 15 2017: (Start)

a(3n) = a(3n+1) = a(3n+2) = a(n).

G.f.: g(x) satisfies g(x) = x + 2 x^2 + (1+x+x^2) g(x^3). (End)

Example

a(1) = 1/(3^0) = 1.

Maple

seq( evalf(floor(n/ (3^floor(log[3](n))))), n=1..500);

Mathematica

Table[IntegerDigits[n, 3][[1]], {n, 110}] (* or *) Table[{PadRight[{}, 3^k, 1], PadRight[ {}, 3^k, 2]}, {k, 0, 4}]//Flatten (* Harvey P. Dale, Mar 12 2023 *)

Crossrefs

Sequence in context: A145705 A029339 A029364 * A079487 A229122 A069010

Adjacent sequences: A122583 A122584 A122585 * A122587 A122588 A122589

Keyword

easy,nonn,base

Author

Peter C. Heinig (algorithms(AT)gmx.de), Oct 20 2006

Extensions

Name changed by Franklin T. Adams-Watters, Sep 29 2011

Status

approved