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
Vincenzo Librandi, Table of n, a(n) for n = 0..21
A. W. F. Edwards, Infinite coprime sequences, Math. Gaz., 48 (1964), 416-422.
A. W. F. Edwards, Infinite coprime sequences, Math. Gaz., 48 (1964), 416-422. [Annotated scanned copy]
R. Mestrovic, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, arXiv preprint arXiv:1202.3670 [math.HO], 2012-2018.
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
More terms from Jeffrey Shallit
Edited by Michael Somos, Feb 01 2004
STATUS
approved