A224533 -id:A224533 - cp's OEIS frontend

A224303 Numbers n for which number of iterations to reach the largest equals number of iterations to reach 1 from the largest in Collatz (3x+1) trajectory of n.

1, 6, 120, 334, 335, 804, 1249, 2008, 2010, 2012, 2013, 6556, 6557, 6558, 6801, 6802, 6803, 7496, 7498, 7500, 7501, 7505, 10219, 22633, 25182, 25183, 27074, 27075, 27864, 27866, 27868, 31838, 31839, 32078, 36630, 36633, 36690, 36691, 36914, 39126, 39344

Offset: 1

Jayanta Basu, Apr 03 2013

nonn

For each n here we have A220421(n) = A222641(n).

			6 is in the list because Collatz trajectory of 6 is {6, 3, 10, 5, 16, 8, 4, 2, 1} and number of steps to reach largest = number of steps to reach 1 from largest = 4.

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

Cf. A220421, A222641, A224533 (odd n).

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3*# + 1] &, n, # > 1 &]; Select[Range[50000],Position[Collatz[#],Max[Collatz[#]]] == {{(Length[Collatz[#]] + 1)/2}} &]

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.

Original entry on oeis.org

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

Offset: 1

T. D. Noe, Apr 23 2013

nonn

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.

			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

Cf. A224533.

cp's OEIS Frontend

A224303 Numbers n for which number of iterations to reach the largest equals number of iterations to reach 1 from the largest in Collatz (3x+1) trajectory of n.

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