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

Author

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

Keywords

• easy
• nonn
• base

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.

Examples

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

Links

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

Programs

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 *)

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)

Extensions

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