OFFSET
0,3
COMMENTS
This sequence is similar to A298011.
LINKS
Rémy Sigrist, Table of n, a(n) for n = 0..8192
FORMULA
a(n) = Sum_{k = 0..A000120(n)-1} A053645^k(n) for any n > 0 (where A053645^k denotes the k-th iterate of A053645).
a(n) >= n with equality iff n = 0 or n = 2^k for some k >= 0.
a(2 * n) = 2 * a(n).
a(2^n - 1) = A000295(n + 1).
a(2 ^ i + n) = a(n) + 2 ^ i + n for 2 ^ i > n. - David A. Corneth, Jan 14 2018
EXAMPLE
For n = 42:
42 = 32 + 8 + 2,
hence a(42) = 1*32 + 2*8 + 3*2 = 54.
PROG
(PARI) a(n) = my (b=binary(n), z=0); for (i=1, #b, if (b[i], b[i] = z++)); return (from digits(b, 2))
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Rémy Sigrist, Jan 11 2018
STATUS
approved