A000546 First occurrence of n consecutive numbers that take same number of steps to reach 1 in 3x+1 problem.

1, 12, 28, 314, 98, 386, 943, 1494, 1680, 4722, 6576, 11696, 3982, 2987, 17548, 36208, 7083, 59692, 159116, 79592, 57857, 212160, 352258, 221185, 57346, 294913, 252548, 530052, 331778, 524289, 1088129, 913319, 2065786, 1541308, 1032875, 1264924, 8151894

Offset: 1

Author

Peter L. Stone [ PetStone(AT)aol.com ]

Keywords

• nonn

Comments

Sequence is precise in the sense that n+1 consecutive numbers starting at a(n) do not take the same number of steps.

Links

• T. D. Noe, Table of n, a(n) for n = 1..100
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A000547.

Programs

Mathematica

Collatz[n_] := Length[NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]] - 1; nn = 10; t = Table[0, {nn}]; t[[1]] = 1; rep = 1; last = 0; n = 1; While[Times @@ t == 0, n++;  r = Collatz[n]; If[r == last, rep++, If[0 < rep <= nn && t[[rep]] == 0, t[[rep]] = n - rep]; last = r; rep = 1]]; t (* T. D. Noe, Jun 20 2012 *)