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

0,2

Comments

Sequence A221469 lists the number of increasing peaks.

Links

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

Example

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.

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]

Prog

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

Crossrefs

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

Sequence in context: A280235 A135765 A222598 * A030669 A030679 A077891

Adjacent sequences: A221467 A221468 A221469 * A221471 A221472 A221473

Keyword

nonn

Author

T. D. Noe, Jan 17 2013

Status

approved