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)) + ...).
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)
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
(Python)
def A198193(n): return sum((n-i)*int(j) for i, j in enumerate(bin(n)[2:])) # Chai Wah Wu, Mar 13 2021
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Brian Reed, Oct 26 2011
STATUS
approved