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 A072944 a(1)=2, a(n+1) = 2*a(n) - phi(a(n)) where phi is the Euler totient function A000010. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified June 1 03:55 EDT 2023. Contains 363068 sequences. (Running on oeis4.)