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Search: id:A066485
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| A066485 |
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Numbers n such that f(n) is a strict local extremum for the prime gaps function f(n) = p(n+1)-p(n), where p(n) denotes the n-th prime; i.e. either f(n)>f(n-1) and f(n)>f(n+1) or f(n)<f(n-1) and f(n)<f(n+1). |
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4
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| 4, 5, 6, 7, 9, 10, 11, 13, 17, 18, 20, 21, 22, 24, 26, 27, 28, 30, 31, 32, 33, 34, 35, 38, 41, 42, 43, 44, 45, 49, 51, 52, 53, 57, 58, 60, 62, 64, 66, 67, 68, 69, 72, 75, 77, 78, 80, 81, 82, 83, 84, 85, 87, 89, 91, 93, 94, 95, 97, 98, 99, 100, 101, 104, 106, 109, 113, 114
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Call a finite subsequence of consecutive terms of a(n) a "zigzag" if it consists of consecutive integers; for example, 30, 31, 32, 33, 34, 35 is a zigzag. Are there zigzags of arbitrary length? (Cf. A066918.)
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EXAMPLE
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4 is a term of a(n) since f(4) is a local maximum: f(3)=2, f(4)=4, f(5)=2.
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MATHEMATICA
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f[n_] := Prime[n+1]-Prime[n]; Select[Range[200], (f[ # ]-f[ #-1])(f[ # ]-f[ #+1])>0&]
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CROSSREFS
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Cf. A066918.
Adjacent sequences: A066482 A066483 A066484 this_sequence A066486 A066487 A066488
Sequence in context: A143789 A068521 A068318 this_sequence A079445 A120173 A075862
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KEYWORD
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nonn
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AUTHOR
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Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Jan 02 2002
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EXTENSIONS
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Edited by Dean Hickerson (dean(AT)math.ucdavis.edu), Jun 26 2002
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