A221470 Least m such that the Collatz (3x+1) iteration of m has exactly n increasing peak values.

1, 5, 3, 7, 15, 287, 191, 127, 223, 159, 143, 95, 63, 47, 31, 27, 703, 6471, 6383, 4255, 6887, 4591, 50427, 47867, 31911, 77671, 161439, 113383, 239231, 159487, 1027431, 974079, 730559, 487039, 432923, 288615, 270271, 3041391, 9158655, 6416623, 16786431, 12589823

Offset: 0

Author

T. D. Noe, Jan 17 2013

Keywords

• nonn

Comments

Sequence A221469 lists the number of increasing peaks.

Examples

			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.
		

Links

• T. D. Noe, Table of n, a(n) for n = 0..60

Crossrefs

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

Programs

Haskell

a221470 = (+ 1 ) . fromJust . (`elemIndex` (map a221469 [1..]))
-- Reinhard Zumkeller, Jan 18 2013

Mathematica

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]