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A198192
Replace 2^k in the binary representation of n with n-k (i.e. if n = 2^a + 2^b + 2^c + ... then a(n) = (n-a) + (n-b) + (n-c) + ...).
2
0, 1, 1, 5, 2, 8, 9, 18, 5, 15, 16, 29, 19, 34, 36, 54, 12, 30, 31, 52, 34, 57, 59, 85, 41, 68, 70, 100, 75, 107, 110, 145, 27, 61, 62, 99, 65, 104, 106, 148, 72, 115, 117, 163, 122, 170, 173, 224, 87, 138, 140, 194, 145, 201, 204, 263, 156, 216, 219, 282, 226
OFFSET
0,4
LINKS
FORMULA
a(n) = n*A000120(n) - A073642(n). - Franklin T. Adams-Watters, Oct 22 2011
a(n) = b(n,n) with b(0,k) = 0, b(n,k) = k*(n mod 2) + b(floor(n/2),k-1) for n>0. - Alois P. Heinz, Oct 25 2011
EXAMPLE
a(5) = (5-2) + (5-0) = 8 because 5 = 2^2 + 2^0.
a(7) = (7-2) + (7-1) + (7-0) = 18 because 7 = 2^2 + 2^1 + 2^0.
MAPLE
b:= (n, k)-> `if`(n=0, 0, k*(n mod 2)+b(floor(n/2), k-1)):
a:= n-> b(n, n):
seq(a(n), n=0..100); # Alois P. Heinz, Oct 25 2011
PROG
(MATLAB) % n is number of terms to be computed:
function [B] = predAddition(n)
for i = 0:n
k = i;
c = 0;
s = 0;
while(k ~= 0)
if ((i - c) >= 0)
s = s + mod(k, 2)*(i-c);
end
c = c + 1;
k = (k - mod(k, 2))/2;
end
B(i+1) = s;
end
end
CROSSREFS
Sequence in context: A001062 A187876 A179951 * A046878 A375600 A357114
KEYWORD
nonn,look,base
AUTHOR
Brian Reed, Oct 21 2011
STATUS
approved