A178169 -id:A178169 - cp's OEIS frontend

A178168 Product of the numbers in the Collatz (3x+1) trajectory of n, including n.

1, 2, 153600, 8, 5120, 921600, 704889816350720000, 64, 2486851272085340160000, 51200, 4577206599680000, 11059200, 532480000, 9868457428910080000, 114523513552896000000000, 1024, 12238520320000, 44763322897536122880000

Offset: 1

T. D. Noe, May 21 2010

nonn

Row n of A070165 has the Collatz trajectory of n. It appears that all products are unique. This has been verified for all n < 10^6 and for the 12332052 values of n for which a(n) < 2^1081.

			The Collatz iteration starting with 3 is 3, 10, 5, 16, 8, 4, 2, 1. The product of these numbers is 153600.

T. D. Noe, Table of n, a(n) for n=1..500

Cf. A087226 (LCM of the trajectory), A178169, A178170

Collatz[n_] := NestWhileList[If[EvenQ[ # ], #/2, 3#+1] &, n, #>1 &]; Table[Times@@Collatz[n], {n, 100}]

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

cp's OEIS Frontend

A178168 Product of the numbers in the Collatz (3x+1) trajectory of n, including n.

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