A233904 - OEIS

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A233904

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

0, 0, -1, 1, -3, 1, -2, 4, -7, 1, -4, 6, -8, 4, -3, 11, -15, 1, -8, 10, -14, 6, -5, 17, -20, 4, -9, 17, -17, 11, -4, 26, -31, 1, -16, 18, -26, 10, -9, 29, -34, 6, -15, 27, -27, 17, -6, 40, -44, 4

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,5

COMMENTS

For every bit in the binary representation of n, if it is one then add the number represented by the substring left of it, and if it is zero subtract that.

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)), (2*bittest(n,k)-1) * floor(n/2^(k+1)) ) = sum(k=0..A000523(n), (2*A030308(n,k+1)-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) = A233905(n) - A233931(n).

EXAMPLE

27 is 11011 in binary, so we add 1, subtract 11=3, add 110=6, and add 1101=13, so a(27)=17.

PROG

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

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

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

(definec (A233904 n) (cond ((zero? n) n) ((even? n) (- (A233904 (/ n 2)) (/ n 2))) (else (+ (A233904 (/ (- n 1) 2)) (/ (- n 1) 2)))))

;; Antti Karttunen, Dec 21 2013

CROSSREFS

Sequence in context: A250306 A120577 A104695 * A292576 A083275 A230892

Adjacent sequences: A233901 A233902 A233903 * A233905 A233906 A233907

KEYWORD

sign

AUTHOR

Ralf Stephan, Dec 17 2013

STATUS

approved