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 A350369 #20 Oct 25 2022 01:04:27 %S A350369 0,0,2,0,1,2,3,0,3,1,2,2,1,3,4,0,1,3,2,1,1,2,3,2,2,1,6,3,2,4,6,0,2,1, %T A350369 2,3,3,2,3,1,6,1,3,2,1,3,6,2,3,2,2,1,1,6,6,3,3,2,2,4,3,6,6,0,3,2,2,1, %U A350369 1,2,6,3,6,3,2,2,2,3,4,1,3,6,6,1,1,3,3 %N A350369 a(n) is the length of the longest sequence of consecutive tripling steps in the Collatz (3x+1) sequence beginning at n. %C A350369 "Consecutive tripling steps" are repeated (3x+1)/2 operations that are not interrupted by a second division by 2. %C A350369 This sequence attempts to measure the largest upward thrust in each Collatz sequence and so is correlated to some degree with the maximum value (A025586) and length (A006577) of Collatz sequences. %C A350369 If n = 2^x * (2^y*z - 1), then a(n) >= y. - _Charles R Greathouse IV_, Oct 25 2022 %H A350369 Kevin P. Thompson, <a href="/A350369/b350369.txt">Table of n, a(n) for n = 1..10000</a> %H A350369 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a> %e A350369 The Collatz sequence for n=7 has a streak of 3 consecutive tripling steps (at 7, 11, and 17), so a(7) = 3. %e A350369 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1 %e A350369 ^ ^ ^ %o A350369 (PARI) a(n)=my(c,r); n>>=valuation(n,2); while(n>1, n+=(n+1)/2; if(n%2, c++, r=max(r,c+1); n>>=valuation(n,2); c=0)); max(r,c) \\ _Charles R Greathouse IV_, Oct 25 2022 %Y A350369 Cf. A006370, A006577, A006667, A025586, A213215, A221469, A347270, A347409. %K A350369 nonn,easy %O A350369 1,3 %A A350369 _Kevin P. Thompson_, Dec 27 2021