A103745 a(n) = (A102371(n) + n)/2.

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

Offset

1,2

Comments

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.

Links

Table of n, a(n) for n=1..35.

David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [pdf, ps].

David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers, J. Integer Seq. 8 (2005), no. 3, Article 05.3.6, 15 pp.

Formula

a(n) = Sum_{ k>= 1, k == n (mod 2^k) } 2^(k-1). - N. J. A. Sloane and David Applegate, Mar 22 2005

a(n) = A103528(n) + 2^(n-1).

Prog

(PARI) a(n) = 2^(n-1) + sum(k = 1, n-1, if ((n % 2^k) == k, 2^(k-1))); \\ Michel Marcus, May 06 2020

Crossrefs

Cf. A000325, A102371, A103185, A103528.

Sequence in context: A093331 A162216 A032158 * A181586 A112361 A343129

Adjacent sequences: A103742 A103743 A103744 * A103746 A103747 A103748

Keyword

nonn

Author

Philippe Deléham, Mar 26 2005

Extensions

a(27) corrected and more terms from Michel Marcus, May 06 2020

Status

approved