|
|
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 *)
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
(Haskell)
a036467 n = a036467_list !! n
a036467_list = 1 : zipWith (-) a000040_list a036467_list
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy,nice
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|