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
Keywords
Examples
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.
Links
- T. D. Noe, Table of n, a(n) for n = 1..10000
Programs
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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 *)
Formula
From Alan Michael Gómez Calderón, Apr 23 2025: (Start)
Comments