%I #10 Dec 03 2017 07:30:14
%S 1,1,2,3,4,7,10,11,20,31,42,73,110,183,292,473,762,1235,1992,3209,
%T 5198,8407,13604,22011,35614,57625,93238,150863,244100,394963,639054,
%U 1034017,1673070,2707089,4380158,7087241,11467398,18554639,30022036,48576675
%N A Fibonacci-based recurrence.
%H E. S. Rowland, <a href="http://arxiv.org/abs/0710.3217">A natural prime-generating recurrence</a>, arXiv:0710.3217 [math.NT]
%F a(n) = a(n-1) + a(n-2) + gcd(n,a(n-1)) - gcd(n,a(n-2)).
%F a(n) ~ c * phi^n, where phi = A001622 = (1 + sqrt(5))/2 is the golden ratio and c = 0.3434866160389779937344617212678945874922532000472607933856634329169... - _Vaclav Kotesovec_, Dec 03 2017
%p A139759 := proc(n) option remember ; if n <= 1 then 1; else an_1 := A139759(n-1) ; an_2 := A139759(n-2) ; an_1+an_2+gcd(n,an_1)-gcd(n,an_2) ; fi ; end: seq(A139759(n),n=0..60) ; # _R. J. Mathar_, May 20 2008
%t a[0]=a[1]=1; a[n_] := a[n] = a[n-1]+a[n-2]+GCD[n, a[n-1]] - GCD[n, a[n-2]];
%t Table[a[n], {n, 0, 60}] (* _Jean-François Alcover_, Dec 03 2017 *)
%Y Cf. A000045.
%K easy,nonn
%O 0,3
%A _Ctibor O. Zizka_, May 20 2008
%E More terms from _R. J. Mathar_, May 20 2008
%E Converted reference to link - _R. J. Mathar_, Oct 30 2009