|
%I #15 Aug 08 2023 12:22:10
%S 2,3,4,6,10,16,24,40,64,96,160,256,384,640,1024,1536,2560,4096,6144,
%T 10240,16384,24576,40960,65536,98304,163840,262144,393216,655360,
%U 1048576,1572864,2621440,4194304,6291456,10485760,16777216,25165824
%N a(1)=2, a(n+1) = 2*a(n) - phi(a(n)) where phi is the Euler totient function A000010.
%C For any x=f(1) positive integer>1 there is an integer N(x) such that for any n>=N(x) f(n)/f(n-3)=4. N(2)=6 N(3)=5 N(4)=5 ... N(1479) =20. Conjecture: N(x) is asymptotic to C*Log(x) with C=0.3..... ( 3/10 < C < 4/10).
%H Robert Israel, <a href="/A072944/b072944.txt">Table of n, a(n) for n = 1..4978</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 4).
%F a(1)=2, a(2)=3, a(3)=4, a(4)=6, a(5)=10 and for n> 5 a(n) = 4*a(n-3).
%F G.f.: (1+x)/2 + (3 + 5*x + 8*x^2)/(2*(1-4*x^3)). - _Robert Israel_, Dec 09 2019
%p 2,3,seq(op([2^(2*n),3*2^(2*n-1),5*2^(2*n-1)]), n=1..20); # _Robert Israel_, Dec 09 2019
%t NestList[2*#-EulerPhi[#]&,2,40] (* _Harvey P. Dale_, Oct 30 2013 *)
%Y Cf. A000010.
%K easy,nonn
%O 1,1
%A _Benoit Cloitre_, Aug 14 2002
|
