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A095114
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a(1)=1. a(n) = a(n-1) + (number of elements of {a(1),...,a(n-1)} which are <= n-1).
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4
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1, 2, 4, 6, 9, 12, 16, 20, 24, 29, 34, 39, 45, 51, 57, 63, 70, 77, 84, 91, 99, 107, 115, 123, 132, 141, 150, 159, 168, 178, 188, 198, 208, 218, 229, 240, 251, 262, 273, 285, 297, 309, 321, 333, 345, 358, 371, 384, 397, 410, 423, 437, 451, 465, 479, 493, 507, 522
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Every positive integer is either of the form a(n)+n-1 or of the form a(n+1)-a(n)+n, but not both.
The keyword "more" refers to the fact that it would be nice to have the sequences a(n)+n-1 and a(n+1)-a(n)+n in the OEIS too. - N. J. A. Sloane (njas(AT)research.att.com).
Equals A001463 + 1, the partial sums of Golomb's sequence A001462. - Ralf Stephan, May 28 2004
A001462(a(n)) = n and A001462(m) < m for m < a(n). [Reinhard Zumkeller, Feb 09 2012]
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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EXAMPLE
| 3 elements of {a(1),...,a(4)} are <= 4, so a(5) = a(4) + 3 = 9.
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MATHEMATICA
| a[1]=1; a[n_]:=a[n]=a[n-1]+Length[Select[a/@Range[n-1], #<n&]]
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PROG
| (Haskell)
a095114 n = a095114_list !! (n-1)
a095114_list = 1 : f [1] 1 where
f xs@(x:_) k = y : f (y:xs) (k+1) where
y = x + length [z | z <- xs, z <= k]
-- Reinhard Zumkeller, Feb 09 2012
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CROSSREFS
| Equals A001463(n)+1.
Sequence in context: A105434 A145196 A061536 * A062048 A194174 A168048
Adjacent sequences: A095111 A095112 A095113 * A095115 A095116 A095117
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KEYWORD
| nonn,changed
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AUTHOR
| Dean Hickerson (dean.hickerson(AT)yahoo.com), following a suggestion of Leroy Quet May 28 2004
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