|
|
A002715
|
|
An infinite coprime sequence defined by recursion.
(Formerly M2683 N1073)
|
|
5
|
|
|
3, 7, 23, 47, 1103, 2207, 2435423, 4870847, 11862575248703, 23725150497407, 281441383062305809756861823, 562882766124611619513723647, 158418504200047111075388369241884118003210485743490303
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
Every term is relatively prime to all others.
|
|
REFERENCES
|
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
LINKS
|
|
|
FORMULA
|
a(2n+1) = 2*a(2n)+1, a(2n) = (a(2n-1)^2-3)/2, with a(0)=3.
|
|
MATHEMATICA
|
a[n_?OddQ] := a[n] = 2*a[n-1] + 1; a[n_?EvenQ] := a[n] = (a[n-1]^2 - 3)/2; a[0] = 3; Table[a[n], {n, 0, 12}] (* Jean-François Alcover, Jan 25 2013 *)
|
|
PROG
|
(PARI) a(n)=if(n<1, 3*(n==0), if(n%2, 2*a(n-1)+1, (a(n-1)^2-3)/2))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|