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 A233931 a(2n) = a(n) + n, a(2n+1) = a(n), with a(0)=0. 3
 0, 0, 1, 0, 3, 1, 3, 0, 7, 3, 6, 1, 9, 3, 7, 0, 15, 7, 12, 3, 16, 6, 12, 1, 21, 9, 16, 3, 21, 7, 15, 0, 31, 15, 24, 7, 30, 12, 22, 3, 36, 16, 27, 6, 34, 12, 24, 1, 45, 21, 34, 9, 42, 16, 30, 3, 49, 21, 36, 7, 45, 15, 31, 0, 63, 31, 48, 15, 58, 24, 42, 7, 66, 30, 49, 12, 60, 22, 42, 3, 76, 36, 57 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS For every zero 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 FORMULA a(n) = sum(k=0..floor(log(n)/log(2)), (1-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) - A233905(n). EXAMPLE 17 is 10001 in binary, so we add 1, 10=2, and 100=4 so a(17)=7. 27 is 11011 in binary, so we add 11=3, so a(27)=3. PROG (PARI) a(n)=sum(k=0, floor(log(n)/log(2)), (1-bittest(n, k))*floor(n/2^(k+1))) (PARI) a(n)=b=binary(n); sum(k=1, #b, (!b[k])*sum(i=1, k-1, b[i]*2^(k-1-i))) (PARI) a(n)=if(n<1, 0, if(n%2, a(n\2), a(n/2)+n/2)) (Scheme, with memoizing definec-macro from Antti Karttunen's IntSeq-library) (definec (A233931 n) (cond ((zero? n) n) ((even? n) (+ (A233931 (/ n 2)) (/ n 2))) (else (A233931 (/ (- n 1) 2))))) ;; Antti Karttunen, Dec 21 2013 CROSSREFS Sequence in context: A174233 A079530 A020815 * A280725 A243328 A243332 Adjacent sequences:  A233928 A233929 A233930 * A233932 A233933 A233934 KEYWORD nonn AUTHOR Ralf Stephan, Dec 18 2013 STATUS approved

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Last modified September 16 09:01 EDT 2019. Contains 327093 sequences. (Running on oeis4.)