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Search: id:A089401
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(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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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
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FORMULA
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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<k<=2^m: a(2^m + k) = a(k) + 2^m - 1. (Hanna)
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EXAMPLE
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a(6)=5 since 7 - A089398(2^7 + 6) = 7 - 2 = 5.
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MATHEMATICA
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f[n_] := Block[{lg = Floor[Log[2, n]] + 1}, Sum[ Join[ Reverse[ IntegerDigits[n - i + 1, 2]], {0}][[i]], {i, lg}]]; Table[n - f[2^n + n] + 2, {n, 0, 72}] (from Robert G. Wilson v Mar 29 2005)
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PROGRAM
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(PARI) a(n)=n/2+1/2*sum(k=1, n, (-1)^floor((n-k)/2^(k-1))) (Cloitre)
(PARI) {a(n)=if(n<=0, 0, m=floor(log(n)/log(2)); if(n-2^m<=m, n-m+a(n-2^m), 2^m-1+a(n-2^m)))} (Hanna)
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CROSSREFS
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Cf. A089398, A089400.
Sequence in context: A063201 A039858 A035558 this_sequence A035044 A096135 A092829
Adjacent sequences: A089398 A089399 A089400 this_sequence A089402 A089403 A089404
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Oct 30 2003
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EXTENSIONS
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More terms from Benoit Cloitre (benoit7848c(AT)orange.fr) and Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 28 2005
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