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Search: id:A007442
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| A007442 |
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Inverse binomial transform of primes.
(Formerly M0065)
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+0
5
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| 2, 1, 1, -1, 3, -9, 23, -53, 115, -237, 457, -801, 1213, -1389, 445, 3667, -15081, 41335, -95059, 195769, -370803, 652463, -1063359, 1570205, -1961755, 1560269, 1401991, -11023119, 36000427, -93408425, 214275735, -450374071
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(n) is the (n-1)-st difference of the first n primes. Although the magnitude of the terms appears to grow exponentially, a plot shows that the sequence a(n)/2^n has quite a bit of structure. See A082594 for an interesting application. - T. D. Noe (noe(AT)sspectra.com), May 09 2003
Graph this divided by A122803 using plot2 ! - Franklin T. Adams-Watters
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Franklin T. Adams-Watters, Table of n, a(n) for n = 1..1000
T. D. Noe, Plot of A007442
N. J. A. Sloane, Transforms
Eric Weisstein's World of Mathematics, Binomial Transform
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FORMULA
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a(n) = Sum_{k=0..n-1} (-1)^(n-k-1) binomial(n-1, k) prime(k+1)
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EXAMPLE
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a(4) = 7 - 3*5 + 3*3 - 2 = -1.
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MATHEMATICA
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Diff[lst_List] := Table[lst[[i + 1]] - lst[[i]], {i, Length[lst] - 1}]; n=1000; dt = Prime[Range[n]]; a = Range[n]; a[[1]] = 2; Do[dt = Diff[dt]; a[[i]] = dt[[1]], {i, 2, n}]; a
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CROSSREFS
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Cf. A082594.
Sequence in context: A124560 A112707 A054252 this_sequence A054772 A085384 A067856
Adjacent sequences: A007439 A007440 A007441 this_sequence A007443 A007444 A007445
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KEYWORD
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sign,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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