A237661 -id:A237661 - cp's OEIS frontend

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

Kival Ngaokrajang, Feb 11 2014

nonn

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

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

Cf. A002450, A237661, A238192, A238193.

{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 *)

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

(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

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

A238193 Position of first occurrence of (4^n - 1)/3 in A238192.

Original entry on oeis.org

3, 21, 75, 151, 1365, 5461, 14563, 87381, 184111, 932067

Offset: 2

T. D. Noe, Feb 21 2014

Another version of A237661.

Is this (apart from the missing 1) the same as A054646? - R. J. Mathar, Mar 30 2014

Cf. A002450 ((4^n-1)/3), A070165 (Collatz trajectories), A238192.

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; t = Table[c = Collatz[n]; co = Select[c, OddQ]; If[Length[co] == 1, 0, co[[-2]]], {n, 10000}]; Flatten[Table[Position[t, (4^n - 1)/3, 1, 1], {n, 2, 7}]]

cp's OEIS Frontend

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.

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