A187831 Smallest number m > n such that n occurs in Collatz trajectory starting with m; a(0) = 1 by convention.

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

Offset: 0

Author

Reinhard Zumkeller, Jan 04 2013

Keywords

• nonn

Comments

A070165(a(n),k) = n for some k with 1 <= k <= A006577(a(n)).

Examples

			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.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A177729, A061641.

Cf. A225840.

Programs

Haskell

import Data.List (find)
import Data.Maybe (fromJust)
a187831 0 = 1
a187831 n = head $ fromJust $
        find (n `elem`) $ drop (fromIntegral n) a070165_tabf

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 *)