A178168 -id:A178168 - cp's OEIS frontend

A178169 Numbers in A178168, sorted.

1, 2, 8, 64, 1024, 5120, 32768, 51200, 153600, 921600, 1024000, 2097152, 11059200, 40960000, 44040192, 265420800, 268435456, 532480000, 1849688064, 3276800000, 12740198400, 13844480000, 68719476736, 155373797376, 524288000000

Offset: 1

T. D. Noe, May 21 2010

nonn

At least the first 12332052 terms of this sequence are unique. It is conjectured that all terms are unique. The sequence is easy to compute by generating the Collatz tree on the fly while keeping track of products.

T. D. Noe, Table of n, a(n) for n=1..1000

A178170 The product of the numbers in the Collatz trajectory of a(n) is the n-th largest such product.

Original entry on oeis.org

1, 2, 4, 8, 16, 5, 32, 10, 3, 6, 20, 64, 12, 40, 21, 24, 128, 13, 42, 80, 48, 26, 256, 84, 160, 52, 96, 85, 17, 168, 53, 512, 104, 320, 192, 34, 170, 106, 11, 336, 208, 68, 1024, 384, 22, 35, 640, 340, 212, 7, 69, 136, 44, 672, 416, 70, 14, 341, 213, 113, 768, 2048, 1280

Offset: 1

T. D. Noe, May 21 2010

nonn

That is, a(n) is the number k such that A178168(k) = A178169(n).

The sequence is easy to compute by generating the Collatz tree while keeping track of the products at the leaves of the tree. At each step, extend the tree at the leaf having the smallest product.

T. D. Noe, Table of n, a(n) for n=1..1000

A299963 a(n) = greatest prime factor of the terms in the Collatz sequence starting at n; a(1) = 1.

Original entry on oeis.org

1, 2, 5, 2, 5, 5, 17, 2, 17, 5, 17, 5, 13, 17, 53, 2, 17, 17, 29, 5, 7, 17, 53, 5, 29, 13, 1619, 17, 29, 53, 1619, 2, 29, 17, 53, 17, 37, 29, 101, 5, 1619, 7, 43, 17, 17, 53, 1619, 5, 37, 29, 29, 13, 53, 1619, 1619, 17, 43, 29, 101, 53, 61, 1619, 1619, 2, 37

Offset: 1

Rémy Sigrist, Feb 22 2018

nonn

The value 3 cannot appear in this sequence.
The value 1619 appears 1654 times among the first 10000 terms; this is visible as a dashed horizontal line in the corresponding scatterplot.
The most frequent values among the first 10000000 terms are:
Value     Number of occurrences among the first 10000000 terms
  -------   ---------------------------------------------------
   283763   16934
  2017817   15701
     1619   15274
    55667   14706
  2717873    9913

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Ordinal transform of the first 10000000 terms
Index entries for sequences related to 3x+1 (or Collatz) problem

Cf. A006530, A055510, A087272, A178168.

Table[Max[FactorInteger[#][[-1,1]]&/@NestWhileList[If[EvenQ[#],#/2,3#+1]&, n,#>1&]], {n,70}] (* Harvey P. Dale, Jun 22 2020 *)

a(n) = my (g=1); while (n>1, my (f=factor(n)); g=max(g,f[#f~,1]); n=if (n%2, 3*n+1, n/2)); return (g)

a(n) = A006530(A178168(n)).
a(2*n) = a(n) for any n > 1.
a(2^k) = 2 for any k > 0.

cp's OEIS Frontend

A178169 Numbers in A178168, sorted.

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A178170 The product of the numbers in the Collatz trajectory of a(n) is the n-th largest such product.

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A299963 a(n) = greatest prime factor of the terms in the Collatz sequence starting at n; a(1) = 1.

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