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 A299962 #12 Feb 26 2018 19:21:59 %S A299962 1,2,2,3,3,3,3,6,4,4,3,4,12,5,5,6,5,5,24,6,6,7,12,6,6,48,7,7,3,9,24,7, %T A299962 7,96,8,8,9,5,14,48,9,8,192,9,9,3,18,6,18,96,10,9,384,10,10,7,6,36,7, %U A299962 28,192,11,10,768,11,11,12,9,7,72,8,36,384,12,11 %N A299962 Square array T(n, k) read by antidiagonals upwards, n > 0 and k > 0: T(n, k) is the k-th positive number whose Collatz sequence contains n. %C A299962 The n-th row corresponds to indices of rows in A070165 containing n. %H A299962 Rémy Sigrist, <a href="/A299962/a299962.gp.txt">PARI program for A299962</a> %H A299962 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a> %F A299962 T(n, 1) = A070167(n) for any n > 0. %F A299962 T(3*n, k) = 3*n * 2^(k-1) for any n > 0 and k > 0. %F A299962 If the Collatz conjecture is true, then: %F A299962 - T(1, k) = k for any k > 0, %F A299962 - T(2, k) = k+1 for any k > 0. %e A299962 Array T(n, k) begins: %e A299962 n\k| 1 2 3 4 5 6 7 8 9 10 %e A299962 ---+--------------------------------------------------------- %e A299962 1| 1 2 3 4 5 6 7 8 9 10 --> A000027 ? %e A299962 2| 2 3 4 5 6 7 8 9 10 11 %e A299962 3| 3 6 12 24 48 96 192 384 768 1536 --> A007283 %e A299962 4| 3 4 5 6 7 8 9 10 11 12 %e A299962 5| 3 5 6 7 9 10 11 12 13 14 %e A299962 6| 6 12 24 48 96 192 384 768 1536 3072 --> A091629 %e A299962 7| 7 9 14 18 28 36 37 43 49 56 %e A299962 8| 3 5 6 7 8 9 10 11 12 13 %e A299962 9| 9 18 36 72 144 288 576 1152 2304 4608 %e A299962 10| 3 6 7 9 10 11 12 13 14 15 %o A299962 (PARI) See Links section. %Y A299962 Cf. A000027, A007283, A091629, A070165, A070167. %K A299962 nonn,tabl %O A299962 1,2 %A A299962 _Rémy Sigrist_, Feb 22 2018