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 A187831 Smallest number m > n such that n occurs in Collatz trajectory starting with m; a(0) = 1 by convention. 3
 1, 2, 3, 6, 5, 6, 12, 9, 9, 18, 11, 14, 24, 14, 18, 30, 17, 18, 36, 25, 22, 42, 25, 27, 48, 33, 28, 54, 36, 33, 60, 41, 42, 66, 36, 41, 72, 43, 39, 78, 41, 54, 84, 57, 50, 90, 47, 54, 96, 57, 66, 102, 56, 54, 108, 73, 57, 114, 59, 78, 120, 62, 82, 126, 75 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A070165(a(n),k) = n for some k with 1 <= k <= A006577(a(n)). LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 Index entries for sequences related to 3x+1 (or Collatz) problem EXAMPLE n = 10: row 11 of A070165 = [11,34,17,52,26,13,40,20,10,5,16,8,4,2,1], therefore A070165(11,9) = 10 and a(10) = 11; n = 11: rows 12 and 13 of A070165 don't contain 11, but 14 does: row 12: [12,6,3,10,5,16,8,4,2,1], row 13: [13,40,20,10,5,16,8,4,2,1], row 14: [14,7,22,11,34,17,52,26,13,40,20,10,5,16,8,4,2,1], therefore A070165(14,4) = 11: a(11) = 14. MATHEMATICA mcollQ[n_, k_]:=MemberQ[NestWhileList[If[EvenQ[#], #/2, 3#+1]&, n, #>1&], k]==True; Prepend[Table[i=n+1; While[!mcollQ[i, n], i++]; i, {n, 64}], 1] (* Jayanta Basu, May 27 2013 *) Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; Join[{1}, Table[k = n + 1; While[! MemberQ[Collatz[k], n], k++]; k, {n, 100}]] (* T. D. Noe, May 28 2013 *) PROG (Haskell) import Data.List (find) import Data.Maybe (fromJust) a187831 0 = 1 a187831 n = head \$ fromJust \$ find (n `elem`) \$ drop (fromIntegral n) a070165_tabf CROSSREFS Cf. A177729, A061641. Cf. A225840. Sequence in context: A242314 A242311 A097723 * A087786 A210468 A080950 Adjacent sequences: A187828 A187829 A187830 * A187832 A187833 A187834 KEYWORD nonn AUTHOR Reinhard Zumkeller, Jan 04 2013 STATUS approved

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Last modified May 30 01:11 EDT 2023. Contains 363044 sequences. (Running on oeis4.)