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

Author

Jayanta Basu, Mar 06 2013

Keywords

• nonn
• tabf

Comments

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

Examples

			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}
		

Links

• T. D. Noe, Rows n = 1..200 of irregular triangle, flattened
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A070165, A159999.

Programs

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

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 *)