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
T. D. Noe, Table of n, a(n) for n = 0..2000
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
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
More terms from Jud McCranie
STATUS
approved