A213678 Number of terms k such that difference between halving and tripling steps in Collatz (3x+1) trajectory of k is n.

1, 1, 1, 3, 3, 5, 8, 14, 20, 29, 40, 59, 87, 130, 196, 294, 439, 658, 985, 1459, 2203, 3328, 5001, 7482, 11205, 16805, 25220, 37850, 56713, 85108, 127728, 191635

Offset: 0

Author

Jayanta Basu, Mar 04 2013

Keywords

• nonn

Examples

			a(5) = 5 since there are only five numbers 12, 13, 20, 21, 32 such that difference between number of halving and tripling steps is 5.
		

Crossrefs

Cf. A220071, A222599 (lists of numbers).

Programs

Mathematica

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; nn = 15; t = Table[0, {nn}]; Do[c = Collatz[n]; e = Select[c, EvenQ]; diff = 2*Length[e] - Length[c]; If[diff < nn - 1, t[[diff + 2]]++], {n, 2^(nn - 1)}]; t (* T. D. Noe, Mar 04 2013 *)

Extensions

Corrected and extended by T. D. Noe, Mar 06 2013