A103586 a(0)=1, for n > 0: n-th run consists of 2^n-1 copies of n+1.

1, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7

Offset

0,2

Comments

a(A214489(n)) = A070939(A214489(n)).

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

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.

O. Kullmann and X. Zhao, Bounds for variables with few occurrences in conjunctive normal forms, arXiv preprint arXiv:1408.0629 [math.CO], 2014-2017.

Ana Luzón, Manuel A. Morón, and Luis Felipe Prieto-Martínez, Commutators and commutator subgroups of the Riordan group, (2021).

Index entries for sequences related to binary expansion of n

Formula

a(n) = A070939(n + A070939(n)) for n > 0. - Reinhard Zumkeller, Jul 21 2012

Mathematica

Join[{1}, Flatten[Table[PadRight[{}, 2^n-1, n+1], {n, 6}]]] (* Harvey P. Dale, Aug 22 2021 *)

Prog

(Haskell)
a103586 n = a070939 (n + a070939 n)
a103586_list = 1 : concat
   (zipWith (replicate . fromInteger) (tail a000225_list) [2..])
-- Reinhard Zumkeller, Jul 21 2012

Crossrefs

Number of bits in binary representation of A102370(n).

Cf. A000225.

Sequence in context: A081288 A130256 A335741 * A194847 A262070 A117806

Adjacent sequences: A103583 A103584 A103585 * A103587 A103588 A103589

Keyword

nonn,base,easy

Author

Benoit Cloitre, Mar 24 2005

Extensions

a(0) = 1 added, definition and offset adjusted by Reinhard Zumkeller, Jul 21 2012

Status

approved