A214614 Irregular triangle read by rows: row n gives numbers <= n whose Collatz trajectory contains the trajectory of n.

1, 1, 2, 1, 2, 3, 1, 2, 4, 1, 2, 4, 5, 1, 2, 3, 4, 5, 6, 1, 2, 4, 5, 7, 1, 2, 4, 8, 1, 2, 4, 5, 7, 8, 9, 1, 2, 4, 5, 8, 10, 1, 2, 4, 5, 8, 10, 11, 1, 2, 3, 4, 5, 6, 8, 10, 12, 1, 2, 4, 5, 8, 10, 13, 1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 1, 2, 4, 5, 8, 10, 15

Offset

1,3

Comments

Each row has A159999(n) elements and ends in n.

Links

T. D. Noe, Rows n = 1..200 of irregular triangle, flattened

Index entries for sequences related to 3x+1 (or Collatz) problem

Example

Rows of triangle:
{1},
{1, 2},
{1, 2, 3},
{1, 2, 4},
{1, 2, 4, 5},
{1, 2, 3, 4, 5, 6},
{1, 2, 4, 5, 7},
{1, 2, 4, 8},
{1, 2, 4, 5, 7, 8, 9},
{1, 2, 4, 5, 8, 10}

Mathematica

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; f[n_] := Module[{c = Collatz[n]}, Select[c, # <= n &]]; t = Table[f[n], {n, 20}]; Flatten[t] (* T. D. Noe, Mar 07 2013 *)

Prog

(Haskell)
import Data.List (sort)
a214614 n k = a214614_tabf !! (n-1) (k-1)
a214614_row n = a214614_tabf !! (n-1)
a214614_tabf = zipWith f [1..] a070165_tabf where
                       f v ws = sort $ filter (<= v) ws
-- Reinhard Zumkeller, Sep 01 2014

Crossrefs

Cf. A070165, A159999.

Sequence in context: A264846 A265691 A334430 * A265692 A194976 A195082

Adjacent sequences: A214611 A214612 A214613 * A214615 A214616 A214617

Keyword

nonn,tabf

Author

Jayanta Basu, Mar 06 2013

Status

approved