A198193 Replace 2^k in the binary representation of n with n+(k-L) where L = floor(log(n)/log(2)).
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
Offset: 0
Examples
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.
Programs
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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 -
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 *) -
Python
def A198193(n): return sum((n-i)*int(j) for i,j in enumerate(bin(n)[2:])) # Chai Wah Wu, Mar 13 2021
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