A237660 Consider the Collatz trajectory of n; if all terms except n and 1 are even then a(n) = 0, otherwise a(n) is the last odd number before 1.

0, 0, 5, 0, 0, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 21, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 85, 5, 5, 5, 5, 5, 5, 5, 5, 21, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 85

Offset

1,3

Comments

Records (A002450) and indices of records (A237661) are as following:

Records: 5, 21, 85, 341, 1365, 5461, 21845, ...

Indices: 3, 42, 75, 151, 2730, 7281, 14563, ...

See A238192 and A238193 for a slightly different version. - T. D. Noe, Feb 21 2014

Differs from A238192 at n = 5, 21, 85, 341, 1365, 5461, 21845, ... (A002450 without its two initial terms). - Antti Karttunen, Aug 13 2017

Links

Antti Karttunen, Table of n, a(n) for n = 1..21845

Kival Ngaokrajang, Illustration for n = 1..20

Index entries for sequences related to 3x+1 (or Collatz) problem

Mathematica

{0}~Join~Table[If[AllTrue[#, EvenQ], 0, SelectFirst[Reverse@ #, OddQ]] &@ Most@ Rest@ NestWhileList[If[EvenQ@ #, #/2, (3 # + 1)/2] &, n, # > 1 &], {n, 2, 113}] (* Michael De Vlieger, Aug 14 2017 *)

Prog

(Small Basic)
For nn = 1 To 200
n = nn
c1 = 0
c2 = 0
loop:
m2 = math.Remainder(n, 2)
If m2 = 0 Then
  n = n/2
  c2 = c2 + 1
Else
  n = n*3 + 1
  c2 = 0
EndIf
a[c1] = n
c1 = c1 + 1
If n = 1 Then
   If a[c1-c2-2] = "" then
    a[c1-c2-2] = 0
   EndIf
   TextWindow.Write(a[c1-c2-2]+", ")
   Goto stop
Else
   Goto loop
EndIf
stop:
EndFor
(Scheme)
(define (A237660 n) (let loop ((n (A014682 n)) (last-odd 0)) (if (= 1 n) last-odd (loop (A014682 n) (if (odd? n) n last-odd)))))
(define (A014682 n) (if (even? n) (/ n 2) (/ (+ n n n 1) 2)))
;; Antti Karttunen, Aug 13 2017
(PARI) a(n)=my(k); if(n%2, n=3*n+1); n>>=valuation(n, 2); if(n==1, return(0)); k=n; while(1, n+=(n+1)>>1; n>>=valuation(n, 2); if(n==1, return(k), k=n)) \\ Charles R Greathouse IV, Aug 14 2017

Crossrefs

Cf. A002450, A237661, A238192, A238193.

Sequence in context: A073231 A099223 A233427 * A261852 A254293 A263496

Adjacent sequences: A237657 A237658 A237659 * A237661 A237662 A237663

Keyword

nonn

Author

Kival Ngaokrajang, Feb 11 2014

Extensions

Edited by N. J. A. Sloane, Feb 20 2014

Status

approved