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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, or -1 if 1 is never reached.
1
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
1,3
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)
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
KEYWORD
nonn,easy
AUTHOR
Aidan Simmons, Feb 24 2019
EXTENSIONS
Escape clause added to the definition by Antti Karttunen, Dec 05 2021
STATUS
approved