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A233904 a(2n) = a(n) - n, a(2n+1) = a(n) + n, with a(0)=0. 1
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
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
KEYWORD
sign
AUTHOR
Ralf Stephan, Dec 17 2013
STATUS
approved

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Last modified July 22 22:40 EDT 2024. Contains 374544 sequences. (Running on oeis4.)