This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A127633 #16 Jan 05 2025 19:51:38
%S A127633 1,7,19,25,37,43,55,73,79,97,109,115,127,133,145,151,163,169,181,187,
%T A127633 199,217,223,235,241,259,271,277,289,295,307,313,331,343,349,361,367,
%U A127633 379,385,397,403,421,439,451,457,469,475,487,493,505,511,523,529,541
%N A127633 Pure numbers in the Collatz (3x+1) iteration that are not multiples of 3.
%C A127633 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 A127633 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 A127633 T. D. Noe, <a href="/A127633/b127633.txt">Table of n, a(n) for n=1..10000</a>
%H A127633 Douglas J. Shaw, <a href="https://web.archive.org/web/2024*/https://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 A127633 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 A127633 Cf. A061641.
%K A127633 nonn
%O A127633 1,2
%A A127633 _Gary W. Adamson_, Jan 20 2007
%E A127633 Edited by _N. J. A. Sloane_ and _T. D. Noe_, Oct 16 2007