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Search: id:A153036
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| A153036 |
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Integer parts of the full Stern-Brocot tree. |
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+0
3
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| 1, 0, 2, 0, 0, 1, 3, 0, 0, 0, 0, 1, 1, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 3, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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a(n) = floor(A007305(n+2)/A047679(n)).
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LINKS
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Index entries for sequences related to Stern's sequences
N. J. A. Sloane, Stern-Brocot or Farey Tree
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FORMULA
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a(n) = if n=2^k-1 then k else Log2(n)-1-Log2(2^(Log2(n)+1)-(n+1)), where Log2=A000523.
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EXAMPLE
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a(1): 1;
a(2..3): 1x0, 2;
a(4..7): 2x0, 1x1, 3;
a(8..15): 4x0, 2x1, 1x2, 4;
a(16..31): 8x0, 4x1, 2x2, 1x3, 5;
a(32..63): 16x0, 8x1, 4x2, 2x3, 1x4, 6;
a(64..127): 32x0, 16x1, 8x2, 4x3, 2x4, 1x5, 7;
a(128..255): 64x0, 32x1, 16x2, 8x3, 4x4, 2x5, 1x6, 8;
a(256..511): 128x0, 64x1, 32x2, 16x3, 8x4, 4x5, 2x6, 1x7, 9.
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CROSSREFS
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A130321.
Sequence in context: A144528 A146164 A051510 this_sequence A122950 A116489 A166373
Adjacent sequences: A153033 A153034 A153035 this_sequence A153037 A153038 A153039
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KEYWORD
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nonn,tabf
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 22 2008
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