OFFSET
0,2
COMMENTS
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
Powers of 64. - Alexander Fraebel, Aug 29 2020
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (64).
FORMULA
G.f.: 1/(1-64*x). - Philippe Deléham, Nov 24 2008
a(n) = 63*a(n-1) + 64^(n-1), a(0)=1. - Vincenzo Librandi, Jun 07 2011
E.g.f.: exp(64*x). - Ilya Gutkovskiy, Jul 02 2016
a(n) = 64*a(n-1). - Miquel Cerda, Oct 27 2016
MAPLE
seq(2^(6*n), n=0..14); # Nathaniel Johnston, Jun 26 2011
MATHEMATICA
2^(6 Range[0, 20]) (* or *) NestList[64#&, 1, 20] (* Harvey P. Dale, Sep 28 2011 *)
PROG
(Magma) [2^(6*n): n in [0..20]]; // Vincenzo Librandi, Jun 07 2011
(Maxima) makelist(2^(6*n), n, 0, 20); /* Martin Ettl, Nov 12 2012 */
(PARI) a(n)=64^n \\ Charles R Greathouse IV, Jul 02 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Douglas Winston (douglas.winston(AT)srupc.com), Dec 26 2003
STATUS
approved