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 A347268 #34 Sep 07 2021 04:11:12 %S A347268 2,3,7,9,16,20,21,24,26,31,34,35,39,41,44,45,46,54,55,56,58,60,61,72, %T A347268 73,74,76,77,81,97,98,99,100,101,102,107,123,127,128,129,130,131,132, %U A347268 133,134,142,143,155,160,167,168,169,170,171,172,173,174,177,178,179,188,189 %N A347268 a(n) is the first term of the n-th 3x+1 sequence that shares infinitely many 1's with the 3x+1 sequence that starts at 2. %C A347268 a(n) is the first term of the row a(n) of the square array A347270. %C A347268 Integers m such that A008908(m) == 2 (mod 3). - _Michel Marcus_, Aug 31 2021 %H A347268 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a> %e A347268 From _Michel Marcus_ and _Omar E. Pol_, Aug 31 2021: (Start) %e A347268 Excerpt from A347270 array showing that the 3x+1 sequences that start at 2, 3, 7, 9 and 16 share infinitely many 1's. %e A347268 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, ... %e A347268 3,10, 5,16, 8, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, ... %e A347268 7,22,11,34,17,52,26,13,40,20,10, 5,16, 8, 4, 2, 1, 4, 2, 1, ... %e A347268 9,28,14, 7,22,11,34,17,52,26,13,40,20,10, 5,16, 8, 4, 2, 1, ... %e A347268 16, 8, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, ... (End) %o A347268 (PARI) f(n) = if (n%2, 3*n+1, n/2); \\ A006370 %o A347268 nb(n) = my(k=1, m=n); while (m!=1, k++; m=f(m)); k; \\ A008908 %o A347268 isok(m) = (nb(m) % 3) == 2; \\ _Michel Marcus_, Aug 31 2021 %Y A347268 Companion of A347267 and A347269. %Y A347268 Cf. A006370, A008908, A033478, A033479, A075884, A076536, A153727, A347270. %K A347268 nonn %O A347268 1,1 %A A347268 _Omar E. Pol_, Aug 25 2021 %E A347268 More terms from _Michel Marcus_, Aug 31 2021