A224537 Least odd number d such that the Collatz iteration of d has the following property: if the length of the iteration is b and the maximum value occurs at c, the ratio c/b is the n-th Farey-like fraction.

1, 3, 5, 215, 21, 1625, 13, 901, 467, 771667051

Offset: 1

Author

T. D. Noe, Apr 23 2013

Keywords

• nonn

Comments

The Farey-like fractions are 1, 1/2, 1/3, 2/3, 1/4, 3/4, 1/5, 2/5, 3/5, 4/5, 1/6, 5/6,.... The numerators/denominators are in A038566/A038567. We conclude (unsurprisingly) that the maximum value of a Collatz iteration usually appears toward the beginning of the iteration.

Examples

			Viewed as an irregular triangle, with 0's for unknown terms:
1
3,
5, 215,
21, 1625,
13, 901, 467, 771667051,
53, 0,
67, 35, 1815, 43641, 97, 0,
141, 23, 90435, 0,
93, 79, 15, 895, 763, 0,
61, 603, 1224211, 0,
37, 267, 59, 8857, 5793, 335737, 60221, 5434799, 0, 0
		

Crossrefs

Cf. A224533.