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A073783
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First differences of composite numbers.
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9
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2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1
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OFFSET
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1,1
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COMMENTS
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Also, the highest common factors of pair of successive composite numbers. - Amarnath Murthy, Jan 31 2003
A073783(n) = A073784(n) + 1.
All terms are 1 or 2. Runs of 1's may be of arbitrary lengths, while the lengths of runs of 2's are 1 or 2. - Zak Seidov, Mar 18 2013
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = A002808(n+1) - A002808(n).
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EXAMPLE
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a(7) = A002808(8) - A002808(7) = 15 - 14 = 1.
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MATHEMATICA
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c[x_] := FixedPoint[x + PrimePi[#] + 1 &, x]; Differences[c /@ Range[106]] (* Jayanta Basu, Jul 09 2013 *)
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PROG
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(Haskell)
a073783 n = a073783_list !! (n-1)
a073783_list = zipWith (-) (tail a002808_list) a002808_list
-- Reinhard Zumkeller, Jan 10 2013
(PARI) m=4; forcomposite(n=6, 1e3, print1(n-m", "); m=n) \\ Charles R Greathouse IV, Mar 20 2013
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CROSSREFS
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Cf. A002808, A073784.
a(n) = A136527(n, n+1).
Cf. A073445 (first differences).
Sequence in context: A331104 A270646 A293540 * A134430 A130658 A014695
Adjacent sequences: A073780 A073781 A073782 * A073784 A073785 A073786
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KEYWORD
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easy,nonn
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AUTHOR
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Lior Manor Aug 11 2002
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STATUS
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approved
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