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Search: id:A072726
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| A072726 |
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Numerator of the rationals >= 1 whose continued fractions consist of only even terms, in ascending order by the sum of the continued fraction terms, and descending by lowest order continued fraction terms to highest. |
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+0
4
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| 1, 2, 4, 5, 6, 9, 9, 12, 8, 13, 17, 22, 13, 20, 22, 29, 10, 17, 25, 32, 25, 38, 40, 53, 17, 28, 38, 49, 32, 49, 53, 70, 12, 21, 33, 42, 37, 56, 58, 77, 33, 54, 72, 93, 58, 89, 97, 128, 21, 36, 54, 69, 56, 85, 89, 118, 42, 69, 93, 120, 77, 118, 128, 169
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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a(2^k + 2^j + m) = 2(k-j)*a(2^j + m) + a(m) when 2^k > 2^j > m >=0. a(0) = 1, a(2^k) = 2(k+1), a(2^k + 1) = 4*k + 1 (k>0), a(2^k - 1) = the (k+1)-th Pell number.
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EXAMPLE
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n: a(n)/A072727 has continued fraction:
0: 1/0 = [infinity]
1: 2/1 = [2]
2: 4/1 = [4]
3: 5/2 = [2;2]
4: 6/1 = [6]
5: 9/2 = [4;2]
6: 9/4 = [2;4]
7: 12/5 = [2;2,2]
8: 8/1 = [8]
9: 13/2 = [6;2]
10: 17/4 = [4;4]
11: 22/5 = [4;2,2]
12: 13/6 = [2;6]
13: 20/9 = [2;4,2]
14: 22/9 = [2;2,4]
15: 29/12= [2;2,2,2]
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CROSSREFS
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Cf. A072727, A071585, A071766, A072728, A072729, A000129.
Sequence in context: A037081 A110277 A104704 this_sequence A005528 A050015 A063656
Adjacent sequences: A072723 A072724 A072725 this_sequence A072727 A072728 A072729
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KEYWORD
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easy,frac,nice,nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jul 09 2002
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