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A306577 Last odd number reached by n before 1 through Collatz iteration, where a(n) = 1 when no other odd number is reached. 0
1, 1, 5, 1, 5, 5, 5, 1, 5, 5, 5, 5, 5, 5, 5, 1, 5, 5, 5, 5, 21, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 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, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 85, 5, 5, 5, 5, 5, 5, 5, 5, 21, 85, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Assuming the Collatz conjecture is true, every a(n) is defined. Each entry in this sequence will be a member of A002450, as these are the odd numbers that result in powers of 2. Due to the abundance of entries equal to 5, one may wish to study the values not equal to 5.

From Michael De Vlieger, Mar 05 2019: (Start)

Indices n of the first appearance of odd k:

        k         n

        1         1

        5         3

       21        21

       85        75

      341       151

     1365      1365

     5461      5461

    21845     14563

    87381     87381

   349525    184111

  1398101    932067

  5592405   5592405 (End)

LINKS

Table of n, a(n) for n=1..101.

EXAMPLE

From Felix Fröhlich, Apr 25 2019: (Start)

For n = 16: The Collatz trajectory of 16 up to the first occurrence of 1 is 16, 8, 4, 2, 1. The trajectory does not include any odd number other than 1, so a(16) = 1.

For n = 42: The Collatz trajectory of 42 up to the first occurrence of 1 is 21, 64, 32, 16, 8, 4, 2, 1. The last odd number occurring before 1 is 21, so a(42) = 21. (End)

MATHEMATICA

Array[If[! IntegerQ@ #, 1, #] &@ SelectFirst[Reverse@ Most@ NestWhileList[If[EvenQ@ #, #/2, 3 # + 1] &, #, # > 1 &], OddQ] &, 100] (* Michael De Vlieger, Mar 05 2019 *)

PROG

(PARI) next_iter(n) = if(n%2==0, return(n/2), return(3*n+1))

a(n) = my(x=n, oddnum=1); while(x!=1, if(x%2==1, oddnum=x); x=next_iter(x)); oddnum \\ Felix Fröhlich, Apr 25 2019

CROSSREFS

Cf. A006370, A002450, A247272, A247346, A247715, A247716.

Sequence in context: A073226 A021198 A275976 * A143969 A198366 A162797

Adjacent sequences:  A306574 A306575 A306576 * A306578 A306579 A306580

KEYWORD

nonn,easy

AUTHOR

Aidan Simmons, Feb 24 2019

STATUS

approved

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Last modified October 16 01:14 EDT 2019. Contains 328038 sequences. (Running on oeis4.)