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A103745
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a(n) = (A102371(n) + n)/2.
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4
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1, 2, 5, 8, 17, 34, 65, 128, 257, 514, 1029, 2048, 4097, 8194, 16385, 32768, 65537, 131074, 262149, 524296, 1048577, 2097154, 4194305, 8388608, 16777217, 33554434, 67108869, 134217728, 268435457, 536870914, 1073741825, 2147483648, 4294967297, 8589934594, 17179869189
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OFFSET
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1,2
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COMMENTS
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Values of A103185 (first zero omitted) which are >= a new power of 2 . The initial values of A103185 are 0*, 1*, 2*, 1, 0, 5*, 2, 1, 0, 1, 2, 1, 8*, 5, 2, 1, ... and the starred terms are those which exceed the next power of 2 . Their indices (except for the zero term) are given by A000325.
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LINKS
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David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [pdf, ps].
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FORMULA
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PROG
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(PARI) a(n) = 2^(n-1) + sum(k = 1, n-1, if ((n % 2^k) == k, 2^(k-1))); \\ Michel Marcus, May 06 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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