A122586 - OEIS

%I #23 Mar 12 2023 10:37:14

%S 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,

%T 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,

%U 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

%N Leading digit of n expressed in base 3.

%C 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.

%H Robert Israel, <a href="/A122586/b122586.txt">Table of n, a(n) for n = 1..10000</a>

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

%F From _Robert Israel_, Mar 15 2017: (Start)

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

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

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

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

%t 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 *)

%K easy,nonn,base

%O 1,2

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

%E Name changed by _Franklin T. Adams-Watters_, Sep 29 2011