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Search: id:A100710
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| A100710 |
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Characterized by a(n) XOR (a(n) + 1) = a(n) - n. |
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+0
1
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| 2, 5, 4, 11, 6, 9, 8, 23, 10, 13, 12, 19, 14, 17, 16, 47, 18, 21, 20, 27, 22, 25, 24, 39, 26, 29, 28, 35, 30, 33, 32, 95, 34, 37, 36, 43, 38, 41, 40, 55, 42, 45, 44, 51, 46, 49, 48, 79, 50, 53, 52, 59, 54, 57, 56, 71, 58, 61, 60, 67, 62, 65, 64, 191, 66, 69, 68, 75, 70, 73, 72
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(n) is obtained by "adding 1 to the part of the binary expansion of n-1 to the left of the least significant 0". For example, to work out a(92) first write 91 in binary: 1011011. The part to the left of the least significant 0 is 1011 (eleven), and when we add 1 we get 1100 (twelve). Thus a(92) in binary is 1100011, so a(92)=99. This makes it clear that the map "n goes to a(n)" is a bijection from the positive integers to the positive integers without 1, 3, 7, 15, 31 etc.
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FORMULA
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a(n) = 2*A006519(n) + n - 1.
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CROSSREFS
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Sequence in context: A084432 A071297 A114393 this_sequence A069913 A072403 A010078
Adjacent sequences: A100707 A100708 A100709 this_sequence A100711 A100712 A100713
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Boddington (pbotherstuff(AT)yahoo.co.uk), Apr 09 2006
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