A253720 a(n) = length of row n in A253676 and A254068, assuming the 3x+1 (or Collatz) conjecture.

1, 2, 5, 3, 4, 2, 6, 5, 7, 5, 18, 5, 6, 3, 8, 4, 7, 4, 19, 6, 5, 2, 7, 4, 20, 6, 8, 19, 3, 5, 16, 18, 21, 7, 15, 4, 20, 5, 9, 8, 17, 18, 10, 8, 8, 5, 10, 18, 21, 6, 3, 7, 9, 3, 5, 19, 11, 8, 14, 8, 6, 4, 10, 17, 22, 7

Offset: 1

Author

L. Edson Jeffery, May 02 2015

Keywords

• nonn

Crossrefs

Cf. A253676, A254068.

Programs

Mathematica

(* Row lengths of A253676 and A254068: *)
v[n_] := IntegerExponent[n, 2]; f[x_] := (3*x + 1)/2^v[3*x + 1]; s[x_] := (3 + (3/2)^v[1 + f[x]]*(1 + f[x]))/6; A253676[n_] := NestWhileList[s[4*# - 3] &, n, # > 1 &]; Table[Length[A253676[n]], {n, 1, 66}]

Formula

For n>1, k>=1, a(n) = a((8+(3*n-2)*4^k)/12).