

A213209


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


1



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
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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: A322523 A333210 A285193 * A049850 A319954 A050949
Adjacent sequences: A213206 A213207 A213208 * A213210 A213211 A213212


KEYWORD

nonn


AUTHOR

Jayanta Basu, Mar 02 2013


STATUS

approved



