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A036467
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a(n)+a(n-1) = n-th prime.
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7
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1, 1, 2, 3, 4, 7, 6, 11, 8, 15, 14, 17, 20, 21, 22, 25, 28, 31, 30, 37, 34, 39, 40, 43, 46, 51, 50, 53, 54, 55, 58, 69, 62, 75, 64, 85, 66, 91, 72, 95, 78, 101, 80, 111, 82, 115, 84, 127, 96, 131, 98, 135, 104, 137, 114, 143, 120, 149, 122, 155, 126, 157, 136, 171, 140, 173
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| After the initial 1,1, this sequence contains no duplicate values: terms thereafter have opposite parity, and a(n+2) > a(n). Do even and odd values trade the lead infinitely often? (We would expect them to 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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MATHEMATICA
| a[n_] := Abs[1+Sum[(-1)^(k+1)*Prime[k], {k, 2, n}]]; a /@ Range[0, 65] (* From Jean-François Alcover , Apr 22 2011 *)
t={1, 1}; Do[AppendTo[t, NextPrime[t[[-2]]+t[[-1]]]-t[[-1]]], {n, 64}]; t (* From Vladimir Joseph Stephan Orlovsky, Jan 26 2012 *)
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PROG
| (MAGMA) [n lt 2 select 1 else NthPrime(n)-NthPrime(n-1)+Self(n-1): n in [0..65]]; // Bruno Berselli, Jun 18 2011
(PARI) print1(t=1); forprime(p=2, 1e3, print1(", ", t=p-t)) \\ Charles R Greathouse IV, Jun 18, 2011
(Haskell)
a036467 n = a036467_list !! n
a036467_list = 1 : zipWith (-) a000040_list a036467_list
-- Reinhard Zumkeller, Nov 02 2011
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CROSSREFS
| Cf. A001223, A008347
Sequence in context: A106442 A091204 A106446 * A006875 A064554 A162425
Adjacent sequences: A036464 A036465 A036466 * A036468 A036469 A036470
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KEYWORD
| nonn,easy,nice
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AUTHOR
| Abdelkader Maghraoui (maghraoui(AT)entpe.fr)
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EXTENSIONS
| More terms from Jud McCranie (JudMcCranie(AT)ugaalum.uga.edu)
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