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 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified December 7 01:49 EST 2023. Contains 367616 sequences. (Running on oeis4.)