A002715 - OEIS

%I M2683 N1073 #35 Dec 19 2021 10:00:58

%S 3,7,23,47,1103,2207,2435423,4870847,11862575248703,23725150497407,

%T 281441383062305809756861823,562882766124611619513723647,

%U 158418504200047111075388369241884118003210485743490303

%N An infinite coprime sequence defined by recursion.

%C Every term is relatively prime to all others.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Vincenzo Librandi, <a href="/A002715/b002715.txt">Table of n, a(n) for n = 0..21</a>

%H A. W. F. Edwards, <a href="https://www.jstor.org/stable/3611702">Infinite coprime sequences</a>, Math. Gaz., 48 (1964), 416-422.

%H A. W. F. Edwards, <a href="/A002715/a002715.pdf">Infinite coprime sequences</a>, Math. Gaz., 48 (1964), 416-422. [Annotated scanned copy]

%H R. Mestrovic, <a href="http://arxiv.org/abs/1202.3670">Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof</a>, arXiv preprint arXiv:1202.3670 [math.HO], 2012-2018.

%F a(2n+1) = 2*a(2n)+1, a(2n) = (a(2n-1)^2-3)/2, with a(0)=3.

%t 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 *)

%o (PARI) a(n)=if(n<1,3*(n==0),if(n%2,2*a(n-1)+1,(a(n-1)^2-3)/2))

%Y Cf. A001685, A003686, A064526.

%K nonn

%O 0,1

%A _N. J. A. Sloane_

%E More terms from _Jeffrey Shallit_

%E Edited by _Michael Somos_, Feb 01 2004