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Search: id:A048735
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| A048735 |
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a(n) = (n AND floor(n/2)), where AND is bitwise and-operator (A004198). |
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+0
3
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| 0, 0, 0, 1, 0, 0, 2, 3, 0, 0, 0, 1, 4, 4, 6, 7, 0, 0, 0, 1, 0, 0, 2, 3, 8, 8, 8, 9, 12, 12, 14, 15, 0, 0, 0, 1, 0, 0, 2, 3, 0, 0, 0, 1, 4, 4, 6, 7, 16, 16, 16, 17, 16, 16, 18, 19, 24, 24, 24, 25, 28, 28, 30, 31, 0, 0, 0, 1, 0, 0, 2, 3, 0, 0, 0, 1, 4, 4, 6, 7, 0, 0, 0, 1, 0, 0, 2, 3, 8, 8, 8, 9
(list; graph; listen)
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OFFSET
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0,7
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COMMENT
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To prove that (n AND floor(n/2)) = (3n-(n XOR 2n))/4 (= A048728(n)/4), we first multiply both sides by 4, to get 2*(n AND 2n) = (3n - (n XOR 2n)), and then rearrange terms: 3n = (n XOR 2n) + 2*(n AND 2n), which fits perfectly to the identity A+B = (A XOR B) + 2*(A AND B) (given by Schroeppel in HAKMEM link).
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LINKS
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Beeler, M., Gosper, R. W. and Schroeppel, R., HAKMEM, ITEM 23 (Schroeppel)
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CROSSREFS
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a(n) = A048728(n)/4. (This was the original definition. AND-formula found Jan 01 2007). Positions of zeros are given by A003714. Cf. A003188, A050600.
Adjacent sequences: A048732 A048733 A048734 this_sequence A048736 A048737 A048738
Sequence in context: A037882 A024865 A025109 this_sequence A102037 A097946 A083926
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen, Apr 26 1999. New formula and more terms added by Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Jan 01 2007.
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