

A214614


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


2



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
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OFFSET

1,3


COMMENTS

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


LINKS



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 !! (n1) (k1)
a214614_row n = a214614_tabf !! (n1)
a214614_tabf = zipWith f [1..] a070165_tabf where
f v ws = sort $ filter (<= v) ws


CROSSREFS



KEYWORD

nonn,tabf


AUTHOR



STATUS

approved



