A306577 Last odd number reached by n before 1 through Collatz iteration, where a(n) = 1 when no other odd number is reached, or -1 if 1 is never reached.

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

Offset: 1

Author

Aidan Simmons, Feb 24 2019

Keywords

• nonn
• easy

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)

Examples

			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)
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..14563
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..87381

Crossrefs

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

Programs

Mathematica

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

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

Extensions

Escape clause added to the definition by Antti Karttunen, Dec 05 2021