A306577 - OEIS

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.

%I #35 Dec 06 2021 03:07:53

%S 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,

%T 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,

%U 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

%N 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.

%C 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.

%C From _Michael De Vlieger_, Mar 05 2019: (Start)

%C Indices n of the first appearance of odd k:

%C k n

%C 1 1

%C 5 3

%C 21 21

%C 85 75

%C 341 151

%C 1365 1365

%C 5461 5461

%C 21845 14563

%C 87381 87381

%C 349525 184111

%C 1398101 932067

%C 5592405 5592405 (End)

%H Antti Karttunen, <a href="/A306577/b306577.txt">Table of n, a(n) for n = 1..14563</a>

%H Antti Karttunen, <a href="/A306577/a306577.txt">Data supplement: n, a(n) computed for n = 1..87381</a>

%e From _Felix Fröhlich_, Apr 25 2019: (Start)

%e 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.

%e 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)

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

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

%o 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

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

%K nonn,easy

%O 1,3

%A _Aidan Simmons_, Feb 24 2019

%E Escape clause added to the definition by _Antti Karttunen_, Dec 05 2021