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A036467 a(n) + a(n-1) = n-th prime. 9
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; text; internal format)
OFFSET
0,3
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.) - Franklin T. Adams-Watters, Jan 25 2010
LINKS
MATHEMATICA
a[n_] := Abs[1+Sum[(-1)^(k+1)*Prime[k], {k, 2, n}]]; a /@ Range[0, 65] (* Jean-François Alcover, Apr 22 2011 *)
t={1, 1}; Do[AppendTo[t, NextPrime[t[[-2]]+t[[-1]]]-t[[-1]]], {n, 64}]; t (* Vladimir Joseph Stephan Orlovsky, Jan 26 2012 *)
Transpose[NestList[{First[#]+1, Prime[First[#]+1]-Last[#]}&, {0, 1}, 70]][[2]] (* Harvey P. Dale, Sep 14 2012 *)
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
CROSSREFS
Sequence in context: A091204 A106446 A321220 * A006875 A064554 A290641
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
More terms from Jud McCranie
STATUS
approved

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Last modified June 20 23:18 EDT 2024. Contains 373535 sequences. (Running on oeis4.)