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 A089401 a(n) = m - A089398(2^m + n) for m>=n. 2
 1, 1, 3, 2, 4, 5, 6, 5, 7, 8, 11, 9, 11, 12, 13, 12, 14, 15, 18, 18, 19, 20, 21, 20, 22, 23, 26, 24, 26, 27, 28, 27, 29, 30, 33, 33, 36, 36, 37, 36, 38, 39, 42, 40, 42, 43, 44, 43, 45, 46, 49, 49, 50, 51, 52, 51, 53, 54, 57, 55, 57, 58, 59, 58, 60, 61, 64, 64, 67, 69, 69, 68, 70 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS A089398(n) = n-th column sum of binary digits of k*2^(k-1), where summation is over all k>=1, without carrying from columns sums that may exceed 2. Row sums of triangular arrays in A103582 and in A103583. - Philippe DELEHAM, Apr 04 2005 LINKS FORMULA a(n)=n/2+1/2*sum(k=1, n, (-1)^floor((n-k)/2^(k-1))) (Cloitre) Let a(0)=0; when n - 2^[log_2(n)] <= [log_2(n)] then a(n) = a(n - 2^[log_2(n)]) + n - [log_2(n)], else a(n) = a(n - 2^[log_2(n)]) + 2^[log_2(n)] - 1. Thus a(2^m) = 2^m - m for all m>=0; for 0<=k<=m: a(2^m + k) = a(k) + 2^m + k - m; for m

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Last modified May 22 20:37 EDT 2013. Contains 225583 sequences.