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 A062054 Numbers with 4 odd integers in their Collatz (or 3x+1) trajectory. 4
 17, 34, 35, 68, 69, 70, 75, 136, 138, 140, 141, 150, 151, 272, 276, 277, 280, 282, 300, 301, 302, 544, 552, 554, 560, 564, 565, 600, 602, 604, 605, 1088, 1104, 1108, 1109, 1120, 1128, 1130, 1137, 1200, 1204, 1205, 1208, 1210, 2176, 2208, 2216, 2218, 2240 (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)) = 4; A006667(a(n)) = 3. Numbers m such that (s0 - 4s1)/2m = 1 where s0 is the sum of the even elements and s1 the sum of the odd elements in the Collatz trajectory of m. - Michel Lagneau, Aug 13 2018 If m is in the sequence then so is 2*m, so one would only have to check odd numbers. - David A. Corneth, Aug 13 2018 REFERENCES J. Shallit and D. Wilson, The "3x+1" Problem and Finite Automata, Bulletin of the EATCS #46 (1992) pp. 182-185. LINKS David A. Corneth, Table of n, a(n) for n = 1..15549 (first 750 terms from Reinhard Zumkeller, terms < 10^15) 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. Eric Weisstein's World of Mathematics, Collatz Problem Wikipedia, Collatz conjecture FORMULA The twelve formulas giving this sequence are listed in Corollary 3.3 in J. R. Goodwin with the following caveats: the value x cannot equal zero in formulas (3.16) and (3.20), 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 17 is (17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1), which contains 4 odd integers. - Jeffrey R. Goodwin, Oct 26 2011 MATHEMATICA col4Q[n_]:=Module[{c=NestWhileList[If[EvenQ[#], #/2, 3#+1]&, n, #!=1&]}, Count[c, _?OddQ]==4]; Select[Range, col4Q]  (* Harvey P. Dale, Mar 21 2011 *) PROG (Haskell) import Data.List (elemIndices) a062054 n = a062054_list !! (n-1) a062054_list = map (+ 1) \$ elemIndices 4 a078719_list -- Reinhard Zumkeller, Oct 08 2011 CROSSREFS Cf. A000079, A006370, A062052, A062053, A062055, A062056, A062057, A062058, A062059, A062060, A092893, A198587. Sequence in context: A168579 A135637 A040272 * A164008 A013577 A234942 Adjacent sequences:  A062051 A062052 A062053 * A062055 A062056 A062057 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified October 19 04:40 EDT 2019. Contains 328211 sequences. (Running on oeis4.)