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

1,2

Comments

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

Links

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

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A178911 A227027 A001219 * A076233 A066581 A054776

Adjacent sequences: A224300 A224301 A224302 * A224304 A224305 A224306

Keyword

nonn

Author

Jayanta Basu, Apr 03 2013

Status

approved