A105029 - OEIS

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A105029

Write numbers in binary under each other, left justified, read diagonals in downward direction, convert to decimal.

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; 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.`
	REFERENCES	`David Applegate, Benoit Cloitre, Philippe DELEHAM 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.`
	LINKS	`David Applegate, Benoit Cloitre, Philippe DELEHAM and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [pdf, ps].`
	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.`
	CROSSREFS	`Cf. A102370, A105030, A105025-A105028, A105033.` `Sequence in context: A157890 A198821 A171897 * A190124 A067548 A053793` `Adjacent sequences: A105026 A105027 A105028 * A105030 A105031 A105032`
	KEYWORD	`nonn,base`
	AUTHOR	`Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 03 2005`

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Last modified February 16 10:23 EST 2012. Contains 205904 sequences.