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 A127933 #25 Jan 05 2025 19:51:38 %S A127933 0,0,7,8,16,19,9,17,20,20,7,10,23,111,18,26,21,21,34,8,29,16,11,24, %T A127933 112,112,32,19,107,27,14,22,115,14,35,35,22,9,30,17,17,12,118,25,25, %U A127933 38,113,113,69,33,33,20,20,46,108,46,121,28,28,41,15,15,23,116,116 %N A127933 Number of halving and tripling steps to reach 1 from the n-th pure hailstone number in the '3x+1' problem. %C A127933 Previous name was: A006577(k), k = pure hailstone numbers from A061641. %C A127933 Impure hailstone numbers are those which occur in the trajectories of smaller numbers. Thus 5 is impure since it occurs in the trajectory of 3. %H A127933 Amiram Eldar, <a href="/A127933/b127933.txt">Table of n, a(n) for n = 1..10000</a> %H A127933 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 A127933 a(n) = A006577(A061641(n)). %e A127933 3 is the 3rd term of A061641, the trajectory of 3 has 7 terms: (10, 5, 16, 8, 4, 2, 1), so a(3) = 7. %Y A127933 Cf. A006577, A061641. %K A127933 nonn %O A127933 1,3 %A A127933 _Gary W. Adamson_, Feb 08 2007 %E A127933 Offset corrected and more terms added by _Amiram Eldar_, Feb 28 2020 %E A127933 Name edited by _Michel Marcus_, Feb 28 2020