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Search: id:A075885
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| A075885 |
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a(n) = 1 + n + n[n/2] + n[n/2][n/3] + n[n/2][n/3][n/4] +... where [x]=floor(x). |
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1
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| 1, 2, 5, 10, 29, 46, 169, 239, 745, 1450, 4111, 5182, 27157, 33164, 84001, 186496, 610065, 713474, 3061009, 3526553, 13783421, 27380452, 63264389, 71240523, 444872761, 620729126, 1400231613, 2615011102, 9094701085, 10008828958
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n) ~ L^n where L = 2.2001610580 is the geometric mean of Luroth expansions, where ln(L) = sum_{k=1..inf} ln(k)/[k(k+1)] = 0.7885305659.
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LINKS
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Paul D Hanna, Table of n, a(n) for n = 0..500
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FORMULA
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a(n) = 1 + sum_{m=1..n} product_{k=1..m} floor(n/k) for n>0 and a(0)=1.
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EXAMPLE
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a(5) = 46 = 1 +5[5/2] +5[5/2][5/3] +5[5/2][5/3][5/4] +5[5/2][5/3][5/4][5/5] = 1 + 5 + 5*2 + 5*2*1 + 5*2*1*1 + 5*2*1*1*1.
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CROSSREFS
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Sequence in context: A074801 A006401 A102964 this_sequence A018377 A056363 A006404
Adjacent sequences: A075882 A075883 A075884 this_sequence A075886 A075887 A075888
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KEYWORD
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easy,nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Oct 16 2002
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