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a(n) = (A102371(n) + n)/2.
4

%I #19 Jan 24 2022 08:01:25

%S 1,2,5,8,17,34,65,128,257,514,1029,2048,4097,8194,16385,32768,65537,

%T 131074,262149,524296,1048577,2097154,4194305,8388608,16777217,

%U 33554434,67108869,134217728,268435457,536870914,1073741825,2147483648,4294967297,8589934594,17179869189

%N a(n) = (A102371(n) + n)/2.

%C 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.

%H David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [<a href="http://neilsloane.com/doc/slopey.pdf">pdf</a>, <a href="http://neilsloane.com/doc/slopey.ps">ps</a>].

%H David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL8/Sloane/sloane300.html">Sloping binary numbers: a new sequence related to the binary numbers</a>, J. Integer Seq. 8 (2005), no. 3, Article 05.3.6, 15 pp.

%F a(n) = Sum_{ k>= 1, k == n (mod 2^k) } 2^(k-1). - _N. J. A. Sloane_ and _David Applegate_, Mar 22 2005

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

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

%Y Cf. A000325, A102371, A103185, A103528.

%K nonn

%O 1,2

%A _Philippe Deléham_, Mar 26 2005

%E a(27) corrected and more terms from _Michel Marcus_, May 06 2020