

A213678


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


2



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
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OFFSET

0,4


LINKS



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



KEYWORD

nonn


AUTHOR



EXTENSIONS

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


STATUS

approved



