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 A222599 Irregular array of numbers T(n,k) such that the difference between the number of halving and tripling steps in the Collatz (3x+1) iteration is n. 4
 1, 2, 4, 3, 5, 8, 6, 10, 16, 12, 13, 20, 21, 32, 7, 11, 17, 24, 26, 40, 42, 64, 9, 14, 15, 22, 23, 34, 35, 48, 52, 53, 80, 84, 85, 128, 18, 19, 28, 29, 30, 44, 45, 46, 68, 69, 70, 75, 96, 104, 106, 113, 160, 168, 170, 256, 25, 36, 37, 38, 56, 58, 60, 61, 88 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Note that row n ends with 2^n. The length of row n is A213678(n). LINKS T. D. Noe, Rows n = 0..19 of irregular triangle, flattened EXAMPLE The rows are {1}, {2}, {4}, {3, 5, 8}, {6, 10, 16}, {12, 13, 20, 21, 32}, {7, 11, 17, 24, 26, 40, 42, 64}, {9, 14, 15, 22, 23, 34, 35, 48, 52, 53, 80, 84, 85, 128} MATHEMATICA Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; nn = 10; t = Table[{}, {nn}]; Do[c = Collatz[n]; e = Select[c, EvenQ]; diff = 2*Length[e] - Length[c]; If[diff < nn - 1, AppendTo[t[[diff + 2]], n]], {n, 2^(nn - 1)}]; Flatten[t] CROSSREFS Cf. A213678 (number of terms in each row). Sequence in context: A187790 A307613 A279343 * A249683 A360434 A215898 Adjacent sequences: A222596 A222597 A222598 * A222600 A222601 A222602 KEYWORD nonn,tabf AUTHOR T. D. Noe, Mar 04 2013 STATUS approved

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Last modified June 8 13:24 EDT 2023. Contains 363165 sequences. (Running on oeis4.)