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A089357 a(n) = 2^(6*n).

%I A089357 #58 Sep 08 2022 08:45:12
%S A089357 1,64,4096,262144,16777216,1073741824,68719476736,4398046511104,
%T A089357 281474976710656,18014398509481984,1152921504606846976,
%U A089357 73786976294838206464,4722366482869645213696,302231454903657293676544,19342813113834066795298816
%N A089357 a(n) = 2^(6*n).
%C A089357 For n > 0, numbers M such that a(n) is the highest power of 2 in the Collatz (3x+1) iteration are given by 2^k*(a(n)-1)/3 for any k >= 0. Example: For n = 1, the numbers such that 64 is the highest power of 2 in the Collatz (3x+1) iteration are given by 2^k*(64-1)/3 = 21*2^k for any k >= 0. See A008908 for more information on the Collatz (3x+1) iteration. - _Derek Orr_, Sep 22 2014
%C A089357 Powers of 64. - _Alexander Fraebel_, Aug 29 2020
%H A089357 Vincenzo Librandi, <a href="/A089357/b089357.txt">Table of n, a(n) for n = 0..200</a>
%H A089357 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A089357 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (64).
%F A089357 G.f.: 1/(1-64*x). - _Philippe Deléham_, Nov 24 2008
%F A089357 a(n) = 63*a(n-1) + 64^(n-1), a(0)=1. - _Vincenzo Librandi_, Jun 07 2011
%F A089357 E.g.f.: exp(64*x). - _Ilya Gutkovskiy_, Jul 02 2016
%F A089357 a(n) = A000079(A008588(n)). - _Wesley Ivan Hurt_, Jul 02 2016
%F A089357 a(n) = 64*a(n-1). - _Miquel Cerda_, Oct 27 2016
%p A089357 seq(2^(6*n), n=0..14); # _Nathaniel Johnston_, Jun 26 2011
%t A089357 2^(6 Range[0,20]) (* or *) NestList[64#&,1,20] (* _Harvey P. Dale_, Sep 28 2011 *)
%o A089357 (Magma) [2^(6*n): n in [0..20]]; // _Vincenzo Librandi_, Jun 07 2011
%o A089357 (Maxima) makelist(2^(6*n),n,0,20); /* _Martin Ettl_, Nov 12 2012 */
%o A089357 (PARI) a(n)=64^n \\ _Charles R Greathouse IV_, Jul 02 2016
%Y A089357 Cf. A000079, A000302, A001018, A001025, A008588, A008908, A009976.
%K A089357 nonn,easy
%O A089357 0,2
%A A089357 Douglas Winston (douglas.winston(AT)srupc.com), Dec 26 2003