A224994 Least odd number d such that the Collatz (3x+1) 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 1/n.

1, 3, 5, 21, 13, 53, 67, 141, 93, 61, 37, 149, 101, 65, 261, 173, 693, 461, 305, 209, 813, 541, 2165, 1445, 961, 657, 2315, 1709, 1169, 4557, 3037, 2021, 3659, 5389, 3589, 2413, 5123, 2291, 4253, 2755, 7235, 7557, 5037, 3357, 10123, 8949, 5965, 3973, 15893

Offset

1,2

Comments

This sequence is the first column of the irregular triangle shown in A224537.

For 45 < n <= 300, the length the Collatz sequence of a(n) is 2n. - T. D. Noe, May 01 2013

Links

T. D. Noe, Table of n, a(n) for n = 1..300

Example

The Collatz iteration of 5 is {5, 16, 8, 4, 2, 1}, which has length 6. The maximum occurs at the second position. Note that 2/6 = 1/3. No number less than 5 has this property. Hence a(3) = 5.

Mathematica

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; nn = 50; t = Table[0, {nn}]; t[[1]] = 1; n = 1; While[Times @@ t == 0, n = n + 2; c = Collatz[n]; frac = Position[c, Max[c]][[1, 1]]/Length[c]; numer = Numerator[frac]; denom = Denominator[frac]; If[numer == 1 && denom <= nn && t[[denom]] == 0, t[[denom]] = n]]; t

Crossrefs

Cf. A224537.

Sequence in context: A066902 A007363 A103991 * A321768 A331395 A086175

Adjacent sequences: A224991 A224992 A224993 * A224995 A224996 A224997

Keyword

nonn

Author

T. D. Noe, Apr 23 2013

Status

approved