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A198193 Replace 2^k in the binary representation of n with n+(k-L) where L = floor(log(n)/log(2)). 1
0, 1, 2, 5, 4, 8, 11, 18, 8, 15, 18, 28, 23, 35, 39, 54, 16, 30, 33, 50, 38, 57, 61, 83, 47, 70, 74, 100, 81, 109, 114, 145, 32, 61, 64, 96, 69, 103, 107, 144, 78, 116, 120, 161, 127, 170, 175, 221, 95, 141, 145, 194, 152, 203, 208, 262, 165, 220, 225, 283 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

That is, if n = 2^a + 2^b + 2^c + ... then a(n) = (n+(a-L)) + (n+(b-L)) + (n+(c-L)) + ...).

LINKS

Table of n, a(n) for n=0..59.

FORMULA

Let L = A000523(n), then a(n) = (n-L)*A000120(n) + A073642(n).

EXAMPLE

a(4) = (4+(2-2)) = 4 because int(log(4)/log(2)) = 2 and 4 = 2^2.

a(6) = (6+(2-2)) + (6+(1-2)) = 11 because int(log(6)/log(2)) = 2 and 6 = 2^2 + 2^1.

MAPLE

read("transforms") :

A198193 := proc(n)

        (n-A000523(n))*wt(n)+A073642(n) ;

end proc:

seq(A198193(n), n=0..20) ; # R. J. Mathar, Nov 17 2011

MATHEMATICA

Table[b = Reverse[IntegerDigits[n, 2]]; L = Length[b] - 1; Sum[b[[k]] (n + k - 1 - L), {k, Length[b]}], {n, 0, 59}] (* T. D. Noe, Nov 01 2011 *)

PROG

(MATLAB)

% n is number of terms to be computed, b is the base. The examples all use b=2:

function [V] = revAddition(n, b)

   for i = 0:n

      k = i;

      if (i > 0)

         l = floor(log(i)/log(b));

      end

      s = 0;

      while(k ~= 0)

         if ((i-l) >= 0)

            s = s + mod(k, b)*(i-l);

         end

         l = l - 1;

         k = (k - mod(k, b))/b;

      end

      V(i+1) = s;

   end

end

CROSSREFS

Cf. A000120, A073642, A198192.

Sequence in context: A183542 A328203 A080031 * A316905 A214533 A065221

Adjacent sequences:  A198190 A198191 A198192 * A198194 A198195 A198196

KEYWORD

nonn,base

AUTHOR

Brian Reed, Oct 26 2011

STATUS

approved

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Last modified July 11 20:03 EDT 2020. Contains 335652 sequences. (Running on oeis4.)