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 A062053 Numbers with 3 odd integers in their Collatz (or 3x+1) trajectory. 7
 3, 6, 12, 13, 24, 26, 48, 52, 53, 96, 104, 106, 113, 192, 208, 212, 213, 226, 227, 384, 416, 424, 426, 452, 453, 454, 768, 832, 848, 852, 853, 904, 906, 908, 909, 1536, 1664, 1696, 1704, 1706, 1808, 1812, 1813, 1816, 1818, 3072, 3328, 3392, 3408, 3412, 3413, 3616 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The Collatz (or 3x+1) function is f(x) = x/2 if x is even, 3x+1 if x is odd. The Collatz trajectory of n is obtained by applying f repeatedly to n until 1 is reached. A078719(a(n)) = 3; A006667(a(n)) = 2. REFERENCES J. R. Goodwin, Results on the Collatz Conjecture, Sci. Ann. Comput. Sci. 13 (2003) pp. 1-16 J. Shallit and D. Wilson, The "3x+1" Problem and Finite Automata, Bulletin of the EATCS #46 (1992) pp. 182-185. LINKS Reinhard Zumkeller and David A. Corneth, Table of n, a(n) for n = 1..16191 (first 250 terms from Reinhard Zumkeller, terms < 10^25) J. Shallit and D. Wilson, The "3x+1" Problem and Finite Automata, Bulletin of the EATCS #46 (1992) pp. 182-185. Eric Weisstein's World of Mathematics, Collatz Problem Wikipedia, Collatz conjecture FORMULA The two formulas giving this sequence are listed in Corollary 3.1 and Corollary 3.2 in J. R. Goodwin with the following caveats: the value x cannot equal zero in Corollary 3.2, one must multiply the formulas by all powers of 2 (2^1, 2^2, ...) to get the evens. - Jeffrey R. Goodwin, Oct 26 2011 EXAMPLE The Collatz trajectory of 3 is (3,10,5,16,8,4,2,1), which contains 3 odd integers. MATHEMATICA Collatz[n_?OddQ] := (3n + 1)/2; Collatz[n_?EvenQ] := n/2; oddIntCollatzCount[n_] := Length[Select[NestWhileList[Collatz, n, # != 1 &], OddQ]]; Select[Range[4000], oddIntCollatzCount[#] == 3 &] (* Alonso del Arte, Oct 28 2011 *) PROG (Haskell) import Data.List (elemIndices) a062053 n = a062053_list !! (n-1) a062053_list = map (+ 1) \$ elemIndices 3 a078719_list -- Reinhard Zumkeller, Oct 08 2011 CROSSREFS Cf. A000079, A062052, A062054, A062055, A062056, A062057, A062058, A062059, A062060. Cf. A198584 (this sequence without the even numbers). See also A198587. Sequence in context: A116625 A287560 A318934 * A274652 A339552 A102040 Adjacent sequences:  A062050 A062051 A062052 * A062054 A062055 A062056 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified June 24 21:09 EDT 2021. Contains 345425 sequences. (Running on oeis4.)