

A213181


Number of chains of even numbers of length 2 or more in the Collatz (3x+1) trajectory of n.


2



0, 0, 1, 1, 1, 1, 3, 1, 4, 1, 3, 2, 2, 3, 2, 1, 3, 4, 4, 2, 1, 3, 2, 2, 5, 2, 17, 4, 4, 2, 16, 1, 6, 3, 2, 5, 4, 4, 6, 2, 17, 1, 6, 4, 4, 2, 16, 2, 5, 5, 5, 3, 2, 17, 17, 4, 7, 4, 6, 3, 3, 16, 15, 1, 6, 6, 5, 4, 3, 2, 16, 5, 18, 4, 2, 5, 5, 6, 6, 2, 4, 17, 17
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,7


COMMENTS

A pair of even numbers that appear side by side in Collatz trajectory of n is considered a chain of length 2 and likewise for chains of greater length.


LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000


EXAMPLE

For n=3, Collatz trajectory of 3 is 3,10,5,16,8,4,2,1, hence the only chain is 16,8,4,2 and so a(3)=1; again for 12: 12,6,3,10,5,16,8,4,2,1 and as such there are two chains 12,6 and 16,8,4,2 so a(12)=2


MATHEMATICA

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; Table[c = Collatz[n]; cnt = 0; evenCnt = 0; Do[If[OddQ[i], evenCnt = 0, evenCnt++; If[evenCnt == 2, cnt++]], {i, c}]; cnt, {n, 100}] (* T. D. Noe, Feb 28 2013 *)


CROSSREFS

Cf. A070165.
Sequence in context: A090740 A094603 A165595 * A301848 A325610 A278536
Adjacent sequences: A213178 A213179 A213180 * A213182 A213183 A213184


KEYWORD

nonn


AUTHOR

Jayanta Basu, Feb 28 2013


STATUS

approved



