A217743 Excess of number of odds in the form 4k+1 over number of odds in the form 4k+3 in Collatz trajectory of n.

1, 1, 1, 1, 2, 1, 2, 1, 3, 2, 3, 1, 3, 2, 0, 1, 4, 3, 3, 2, 2, 3, 1, 1, 4, 3, -6, 2, 4, 0, -6, 1, 5, 4, 2, 3, 3, 3, 2, 2, -5, 2, 4, 3, 5, 1, -5, 1, 4, 4, 4, 3, 3, -6, -6, 2, 5, 4, 3, 0, 2, -6, -8, 1, 5, 5, 3, 4, 4, 2, -4, 3, -5, 3, 2, 3, 5, 2, 2, 2, 3, -5, -5

Offset: 1

Author

Jayanta Basu, Mar 23 2013

Keywords

• sign

Links

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

Crossrefs

Cf. A070165, A192719.

Cf. A217744 (n having equal numbers of 4k+1 and 4k+3 terms).

Programs

Mathematica

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3*# + 1] &, n, # > 1 &]; Table[Length[Select[Collatz[n], Mod[#, 4] == 1 &]] - Length[Select[Collatz[n], Mod[#, 4] == 3 &]], {n,60}]
Table[m4=Mod[NestWhileList[If[EvenQ[#],#/2,3*#+1]&,n,#>1&],4];Count[m4, 1]-Count[m4, 3], {n, 60}] (* Zak Seidov, Mar 23 2013 *)