A072944 a(1)=2, a(n+1) = 2*a(n) - phi(a(n)) where phi is the Euler totient function A000010.

2, 3, 4, 6, 10, 16, 24, 40, 64, 96, 160, 256, 384, 640, 1024, 1536, 2560, 4096, 6144, 10240, 16384, 24576, 40960, 65536, 98304, 163840, 262144, 393216, 655360, 1048576, 1572864, 2621440, 4194304, 6291456, 10485760, 16777216, 25165824

Offset

1,1

Comments

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).

Links

Robert Israel, Table of n, a(n) for n = 1..4978

Index entries for linear recurrences with constant coefficients, signature (0, 0, 4).

Formula

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).

G.f.: (1+x)/2 + (3 + 5*x + 8*x^2)/(2*(1-4*x^3)). - Robert Israel, Dec 09 2019

Maple

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

Mathematica

NestList[2*#-EulerPhi[#]&, 2, 40] (* Harvey P. Dale, Oct 30 2013 *)

Crossrefs

Cf. A000010.

Sequence in context: A098855 A143283 A104767 * A024722 A024965 A018142

Adjacent sequences: A072941 A072942 A072943 * A072945 A072946 A072947

Keyword

easy,nonn

Author

Benoit Cloitre, Aug 14 2002

Status

approved