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A014687
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In sequence of odd primes add 1 to first prime, 3rd prime, 5th prime, ... then subtract 1 from 2nd prime, fourth prime, sixth prime and so on.
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9
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4, 4, 8, 10, 14, 16, 20, 22, 30, 30, 38, 40, 44, 46, 54, 58, 62, 66, 72, 72, 80, 82, 90, 96, 102, 102, 108, 108, 114, 126, 132, 136, 140, 148, 152, 156, 164, 166, 174, 178, 182, 190, 194, 196, 200, 210, 224, 226, 230, 232, 240, 240, 252, 256, 264, 268, 272, 276
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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FORMULA
| Also a(n)=prime(n+1)+(-1)^(n+1). - Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Sep 10 2009
Or, odd prime(n)-(-1)^n. - Juri-Stepan Gerasimov (2stepan(AT0rambler.ru), Sep 10 2009
a(n)+a(n-1) = prime(n)+prime(n+1) i.e. a(n) = prime(n)+prime(n+1)-a(n-1) generates sequence with initial value a(1)=4. - Labos E. (labos(AT)ana.sote.hu), Apr 24 2003; corrected by Dean Hickerson (dean.hickerson(AT)yahoo.com), Apr 27 2003
a(n)=A000040(n+1)-A033999(n+1). - Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Sep 10 2009
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EXAMPLE
| a(4)+a(3) = 10+8 = 18 = p(4)+p(5) = 7+11
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MATHEMATICA
| a[1]=4; a[n_] := a[n]=Prime[n]+Prime[n+1]-a[n-1]
Total/@Partition[Riffle[Prime[Range[2, 60]], {1, -1}], 2] (* From Harvey P. Dale, May 19 2011 *)
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CROSSREFS
| Sequence in context: A046558 A180854 * A172022 A152967 A004024 A086663
Adjacent sequences: A014684 A014685 A014686 * A014688 A014689 A014690
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KEYWORD
| nonn,easy
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AUTHOR
| Mohammad K. Azarian (ma3(AT)evansville.edu)
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EXTENSIONS
| More terms from Erich Friedman (erich.friedman(AT)stetson.edu).
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