A223699 Least number whose Collatz (3x+1) iteration has its maximum value at position n (counting from 1).

1, 2, 4, 8, 3, 32, 21, 20, 13, 80, 15, 7, 96, 69, 68, 45, 93, 19, 61, 56, 37, 51, 72, 49, 39, 33, 43, 133, 79, 260, 115, 349, 255, 127, 27, 157, 135, 279, 123, 421, 375, 727, 219, 723, 447, 295, 740, 493, 439, 591, 657, 1281, 1159, 877, 759, 615, 519, 1603

Offset

1,2

Comments

The maximum values are in A223700.

Links

T. D. Noe, Table of n, a(n) for n = 1..800

Example

The Collatz iteration of 15 is {15, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1}. The maximum is 160, which occurs at position 11, counting from the right. Hence, a(11) = 15 because no number smaller than 15 has its maximum value at the 11 position.

Mathematica

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; t= Table[c = Reverse[Collatz[n]]; Position[c, Max[c]][[1, 1]], {n, 10000}]; t2 = {}; n = 0; While[n++; p = Position[t, n, 1, 1]; p != {}, AppendTo[t2, p[[1, 1]]]]; t2

Crossrefs

Cf. A070165 (Collatz iteration of n), A223700.

Sequence in context: A354169 A341811 A332306 * A231610 A225124 A344537

Adjacent sequences: A223696 A223697 A223698 * A223700 A223701 A223702

Keyword

nonn

Author

T. D. Noe, Mar 26 2013

Status

approved