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A162345
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Length of n-th edge in the graph of the zig-zag function for prime numbers.
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8
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2, 2, 2, 3, 3, 3, 3, 3, 5, 4, 4, 5, 3, 3, 5, 6, 4, 4, 5, 3, 4, 5, 5, 7, 6, 3, 3, 3, 3, 9, 9, 5, 4, 6, 6, 4, 6, 5, 5, 6, 4, 6, 6, 3, 3, 7, 12, 8, 3, 3, 5, 4, 6, 8, 6, 6, 4, 4, 5, 3, 6, 12, 9, 3, 3, 9, 10, 8, 6, 3, 5, 7, 7, 6, 5, 5, 7, 6, 6, 9, 6, 6, 6, 4, 5, 5
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OFFSET
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1,1
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COMMENTS
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Also, first differences of A162800.
Also {2, 2, } together with the numbers A052288.
Note that the graph of the zig-zag function for prime numbers is similar to the graph of the mountain path function for prime numbers but with exactly a vertex between consecutive odd noncomposite numbers (A006005).
This is the same as A115061 if n>1 (and also essentially equal to A052288). Proof: Because this is the first differences of A162800, which is {0,2} together with A024675, this sequence (for n>=3) is given by a(n) = (prime(n+1) - prime(n-1))/2. Similarly, because half the numbers between prime(n-1) and prime(n+1) are closer to prime(n) than any other prime, A115061(n) = (prime(n+1) - prime(n-1))/2 for n>=3 as well. - Nathaniel Johnston, Jun 25 2011
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LINKS
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FORMULA
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EXAMPLE
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Array begins:
=====
x, y
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2, 2;
2, 3;
3, 3;
3, 3;
5, 4;
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MAPLE
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MATHEMATICA
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Join[{2, 2}, Table[(Prime[n+1] - Prime[n-1])/2, {n, 3, 100}]] (* Vincenzo Librandi, Dec 19 2016 *)
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PROG
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(Magma) [2, 2] cat[(NthPrime(n+1)-NthPrime(n-1))/2: n in [3..80]]; // Vincenzo Librandi, Dec 19 2016
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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