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A105029 Write numbers in binary under each other, left justified, read diagonals in downward direction, convert to decimal. 5
0, 2, 6, 5, 4, 14, 13, 8, 11, 10, 9, 12, 30, 29, 24, 19, 18, 17, 20, 23, 22, 21, 16, 27, 26, 25, 28, 62, 61, 56, 51, 34, 33, 36, 39, 38, 37, 32, 43, 42, 41, 44, 47, 46, 45, 40, 35, 50, 49, 52, 55, 54, 53, 48, 59, 58, 57, 60, 126, 125, 120, 115, 98, 65, 68, 71, 70 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

All terms are distinct, but the numbers 2^m - 1 are missing.

a(n) = Sum_{k>=1} B(n+k-1,k)*2^(A103586(n)-k) where B(n,k) n>=1, k>=1 is the infinite array:

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...

1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...

1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...

1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...

1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...

1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...

.......

where n-th row consists of binary expansion of n followed by 0's.

a(n) = A105025(n) iff A070939(n) = A103586(n), cf. A214489. - Reinhard Zumkeller, Jul 21 2012

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.

Index entries for sequences related to binary expansion of n

EXAMPLE

0

1

1 0

1 1

1 0 0

1 0 1

1 1 0

1 1 1

1 0 0 0

1 0 0 1

1 0 1 0

and reading the diagonals downwards we get 0, 10, 110, 101, 100, 1110, 1101, etc.

PROG

(Haskell)

import Data.Bits ((.|.), (.&.))

a105029 n = foldl (.|.) 0 $ zipWith (.&.) a000079_list $

   map (\x -> (len + 1 - a070939 x) * x)

       (reverse $ enumFromTo n (n - 1 + len))  where len = a103586 n

-- Reinhard Zumkeller, Jul 21 2012

CROSSREFS

Cf. A102370, A105030, A105025, A105026, A105027, A105028, A105033.

Cf. A000079, A070939, A103586.

Sequence in context: A329932 A198821 A171897 * A309040 A316134 A273621

Adjacent sequences:  A105026 A105027 A105028 * A105030 A105031 A105032

KEYWORD

nonn,base

AUTHOR

Benoit Cloitre, Apr 03 2005

STATUS

approved

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Last modified September 23 09:03 EDT 2020. Contains 337298 sequences. (Running on oeis4.)