Aidan Simmons - cp's OEIS frontend

User: Aidan Simmons

Aidan Simmons has authored 2 sequences.

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

Aidan Simmons, Feb 24 2019

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)

			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)

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

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

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

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

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

A306546 Modified Collatz Map such that odd numbers are treated the same, but even numbers have all factors of 2 removed.

Original entry on oeis.org

4, 1, 10, 1, 16, 3, 22, 1, 28, 5, 34, 3, 40, 7, 46, 1, 52, 9, 58, 5, 64, 11, 70, 3, 76, 13, 82, 7, 88, 15, 94, 1, 100, 17, 106, 9, 112, 19, 118, 5, 124, 21, 130, 11, 136, 23, 142, 3, 148, 25, 154, 13, 160, 27, 166, 7, 172, 29, 178, 15, 184, 31, 190, 1, 196, 33, 202, 17, 208, 35, 214, 9, 220, 37, 226, 19, 232

Offset: 1

Aidan Simmons, Feb 22 2019

All numbers that reach 1 under normal Collatz iteration will reach 1 through this mapping. This sequence combines all consecutive even number halvings into one step. This will decrease steps to completion compared to normal Collatz iteration for all starting points other than 1 and 2, drastically in most cases. If this mapping is applied upon A000265, the sequence generated when the even operation is applied initially, then further iteration through this modified mapping will have all entries synchronize to all either be odd or all be even for any given step.

Cf. A006370, A016777, A000265.

a(n) = if (n%2, 3*n+1, n >> valuation(n, 2)); \\ Michel Marcus, Mar 05 2019

For any even n, a(n) = A000265(n). For any odd n, a(n) = 3n+1.

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User: Aidan Simmons

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.

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