A233905 - OEIS

A233905

a(2n) = a(n), a(2n+1) = a(n) + n, with a(0)=0.

0, 0, 0, 1, 0, 2, 1, 4, 0, 4, 2, 7, 1, 7, 4, 11, 0, 8, 4, 13, 2, 12, 7, 18, 1, 13, 7, 20, 4, 18, 11, 26, 0, 16, 8, 25, 4, 22, 13, 32, 2, 22, 12, 33, 7, 29, 18, 41, 1, 25, 13, 38, 7, 33, 20, 47, 4, 32, 18, 47, 11, 41, 26, 57, 0, 32, 16, 49, 8, 42, 25, 60, 4, 40, 22, 59, 13, 51, 32, 71, 2, 42, 22, 63, 12, 54

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OFFSET

0,6

COMMENTS

For every one bit in the binary representation of n, add the number represented by the substring left of it.

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..8192

Index entries for sequences related to binary expansion of n

FORMULA

a(n) = sum(k=0..floor(log(n)/log(2)), bittest(n,k) * floor(n/2^(k+1)) ) = sum(k=0..A000523(n), A030308(n,k+1) * floor(n/2^(k+1)) ), with bittest(n,k)=0 or 1 according to the k-th bit of n (the zeroth bit the least significant).

a(n) = A011371(n) - A233931(n).

EXAMPLE

27 is 11011 in binary, so we add 1, 110=6, and 1101=13, so a(27)=20.

PROG

(PARI) a(n)=if(n<1, 0, if(n%2, a(n\2)+n\2, a(n/2)))

(PARI) a(n)=sum(k=0, floor(log(n)/log(2)), bittest(n, k)*floor(n/2^(k+1)))

(Scheme, with memoizing definec-macro from Antti Karttunen's IntSeq-library)

(definec (A233905 n) (cond ((zero? n) n) ((even? n) (A233905 (/ n 2))) (else (+ (A233905 (/ (- n 1) 2)) (/ (- n 1) 2)))))

;; Antti Karttunen, Dec 21 2013

CROSSREFS

Sequence in context: A286238 A286237 A059781 * A285284 A288183 A324055

Adjacent sequences: A233902 A233903 A233904 * A233906 A233907 A233908

KEYWORD

nonn

AUTHOR

Ralf Stephan, Dec 17 2013

STATUS

approved