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A008347
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a(n) = sum_{i=0..n-1} (-1)^i prime(n-i).
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9
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0, 2, 1, 4, 3, 8, 5, 12, 7, 16, 13, 18, 19, 22, 21, 26, 27, 32, 29, 38, 33, 40, 39, 44, 45, 52, 49, 54, 53, 56, 57, 70, 61, 76, 63, 86, 65, 92, 71, 96, 77, 102, 79, 112, 81, 116, 83, 128, 95, 132, 97, 136, 103, 138, 113, 144, 119, 150, 121, 156, 125, 158, 135, 172, 139, 174, 143
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Define the sequence b(n) by b(1) = 1; b(n) = 1-(prime(n-1)/prime(n))*b(n-1) if n > 1. Then b(n) = a(n)/prime(n). Does lim b(n) exist? If so, it must equal 1/2. - Joseph L. Pe, Feb 17 2003
This sequence contains no duplicate values; after the initial 0,2, the parity alternates, and a(n+2) > a(n). Do even and odd values trade the lead infinitely often (as would be expected if we model their difference as a random walk)? [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Jan 25 2010]
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LINKS
| T. D. Noe, Table of n, a(n) for n = 0..2000
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FORMULA
| a(n) = prime(n) - a(n-1) for n>=1.
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MAPLE
| A008347 := proc(n) options remember; if n = 0 then 0 else abs(A008347(n-1)-ithprime(n)); fi; end;
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MATHEMATICA
| Join[{0}, Abs[Accumulate[Times@@@Partition[Riffle[Prime[Range[80]], {1, -1}], 2]]]] (* From Harvey P. Dale, Dec 11 2011 *)
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CROSSREFS
| Sequence in context: A074987 A128280 A106625 * A112387 A193174 A076077
Adjacent sequences: A008344 A008345 A008346 * A008348 A008349 A008350
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com) and J. H. Conway (conway(AT)math.princeton.edu)
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