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%I #14 Aug 12 2022 00:34:03
%S 1,7,19,25,37,43,55,73,79,97,109,115,127,133,145,151,163,169,181,187,
%T 199,217,223,235,241,259,271,277,289,295,307,313,331,343,349,361,367,
%U 379,385,397,403,421,439,451,457,469,475,487,493,505,511,523,529,541
%N Pure numbers in the Collatz (3x+1) iteration that are not multiples of 3.
%C The sequence is a list of pure numbers not congruent to 0 mod 3. The remaining pure numbers are congruent to 1 or 7 mod 18.
%C After computing all a(n) < 10^9, the ratio a(n)/n appears to be converging to 10.101... Hence it appears that the numbers in this sequence have a density of about 99/1000. - _T. D. Noe_, Oct 12 2007
%H T. D. Noe, <a href="/A127633/b127633.txt">Table of n, a(n) for n=1..10000</a>
%H Douglas J. Shaw, <a href="http://www.fq.math.ca/Papers1/44-3/quartshaw03_2006.pdf">The Pure Numbers Generated by the Collatz Sequence</a>, The Fibonacci Quarterly, Vol. 44, Number 3, August 2006, p. 194.
%F A positive integer n is pure if its entire tree of preimages under the Collatz function C is greater than or equal to it; otherwise n is impure [Shaw, p. 195]. For n a positive integer, the function C is defined by C(n) = {3n+1, n odd; n/2, n even}.
%Y Cf. A061641.
%K nonn
%O 1,2
%A _Gary W. Adamson_, Jan 20 2007
%E Edited by _N. J. A. Sloane_ and _T. D. Noe_, Oct 16 2007
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