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Least m such that the Collatz (3x+1) iteration of m has exactly n increasing peak values.
2

%I #10 Jan 18 2013 19:19:43

%S 1,5,3,7,15,287,191,127,223,159,143,95,63,47,31,27,703,6471,6383,4255,

%T 6887,4591,50427,47867,31911,77671,161439,113383,239231,159487,

%U 1027431,974079,730559,487039,432923,288615,270271,3041391,9158655,6416623,16786431,12589823

%N Least m such that the Collatz (3x+1) iteration of m has exactly n increasing peak values.

%C Sequence A221469 lists the number of increasing peaks.

%H T. D. Noe, <a href="/A221470/b221470.txt">Table of n, a(n) for n = 0..60</a>

%e The Collatz iteration starting at 7 is (7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1), which has 3 increasing peaks: 22, 34, and 52. No number smaller than 7 has 3 increasing peaks. Hence, a(3) = 7.

%t Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; nn = 20; t = Table[0, {nn}]; found = 0; n = 0; While[found < nn, n++; c = Collatz[n]; cnt = 0; mx = n; Do[If[k > mx, cnt++; mx = k], {k, c}]; If[cnt > 0 && cnt <= nn && t[[cnt]] == 0, t[[cnt]] = n; found++]]; Join[{1}, t]

%o (Haskell)

%o a221470 = (+ 1 ) . fromJust . (`elemIndex` (map a221469 [1..]))

%o -- _Reinhard Zumkeller_, Jan 18 2013

%Y Cf. A070165 (Collatz trajectory of n), A221469.

%K nonn

%O 0,2

%A _T. D. Noe_, Jan 17 2013