A222600 Least number k such that the difference between the number of halving and tripling steps in the Collatz (3x+1) iteration is n.

1, 2, 4, 3, 6, 12, 7, 9, 18, 25, 33, 43, 39, 78, 105, 135, 123, 169, 159, 295, 283, 111, 222, 297, 175, 103, 91, 121, 31, 27, 54, 73, 97, 129, 171, 231, 313, 411, 543, 327, 649, 859, 763, 1017, 1351, 1215, 703, 937, 871, 1161, 2223, 3097, 2631, 3567, 3175, 4233

Offset: 0

Author

T. D. Noe, Mar 04 2013

Keywords

• nonn

Comments

This is the first number in row n of A222599.

Links

• T. D. Noe, Table of n, a(n) for n = 0..264 (searching until the Collatz sequence has a term greater than 2^63)

Crossrefs

Cf. A213678, A222599.

Programs

Mathematica

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; nn = 50; t = Table[0, {nn}]; n = 0; While[Min[t] == 0, n++; c = Collatz[n]; e = Select[c, EvenQ]; diff = 2*Length[e] - Length[c]; If[diff < nn - 1 && t[[diff + 2]] == 0, t[[diff + 2]] = n]]; t