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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 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.)