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

0,4

Links

Table of n, a(n) for n=0..31.

Example

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.

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 *)

Crossrefs

Cf. A220071, A222599 (lists of numbers).

Sequence in context: A200737 A200741 A271970 * A293676 A303714 A098353

Adjacent sequences: A213675 A213676 A213677 * A213679 A213680 A213681

Keyword

nonn

Author

Jayanta Basu, Mar 04 2013

Extensions

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

Status

approved