A213209 Number of isolated even numbers in Collatz (3x+1) trajectory of n.

0, 1, 1, 0, 0, 2, 2, 0, 2, 1, 1, 1, 0, 3, 3, 0, 0, 3, 2, 0, 0, 2, 2, 1, 2, 1, 24, 2, 1, 4, 23, 0, 2, 1, 1, 2, 2, 3, 5, 0, 23, 1, 3, 1, 0, 3, 22, 1, 2, 3, 2, 0, 0, 25, 24, 2, 3, 2, 4, 3, 2, 24, 24, 0, 2, 3, 3, 0, 0, 2, 21, 2, 24, 3, 1, 2, 1, 6, 5, 0, 2, 24, 23, 0

Offset

1,6

Comments

An isolated even is not a member of any even chain in Collatz trajectory of n; see also A213181.

Links

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

Example

a(7)=2 since there are only 2 numbers 22 and 34 in the Collatz trajectory of 7 that are not part of any even chain.

Mathematica

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; Table[c = Collatz[n]; cnt = 0; evenCnt = 0; Do[If[OddQ[i], If[evenCnt == 1, cnt++]; evenCnt = 0, evenCnt++], {i, c}]; cnt, {n, 100}] (* T. D. Noe, Mar 02 2013 *)

Crossrefs

Cf. A213181.

Sequence in context: A333210 A285193 A354947 * A049850 A319954 A050949

Adjacent sequences: A213206 A213207 A213208 * A213210 A213211 A213212

Keyword

nonn

Author

Jayanta Basu, Mar 02 2013

Status

approved