A221469 Number of increasing peak values in the Collatz (3x+1) iteration of n.

0, 0, 2, 0, 1, 2, 3, 0, 3, 1, 2, 1, 1, 3, 4, 0, 1, 3, 2, 0, 1, 2, 3, 0, 2, 1, 15, 2, 1, 4, 14, 0, 1, 1, 2, 1, 1, 2, 4, 0, 14, 1, 2, 1, 1, 3, 13, 0, 1, 2, 2, 0, 1, 15, 13, 0, 2, 1, 3, 3, 1, 14, 12, 0, 1, 1, 2, 0, 1, 2, 12, 0, 13, 1, 2, 1, 1, 4, 4, 0, 1, 14, 12

Offset

1,3

Comments

That is, the number of times that the Collatz iteration of n reaches a new maximum. See A221470 for the first occurrence of each peak count.

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

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.

Mathematica

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; Table[c = Collatz[n]; cnt = 0; mx = n; Do[If[k > mx, cnt++; mx = k], {k, c}]; cnt, {n, 100}]

Prog

(Haskell)
a221469 n = sum $ map fromEnum $ zipWith (>) (tail ts) ts where
   ts = scanl1 max $ a070165_row n
-- Reinhard Zumkeller, Jan 18 2013

Crossrefs

Cf. A070165 (Collatz trajectory of n), A221470.

Sequence in context: A360677 A263833 A308625 * A350369 A117398 A295989

Adjacent sequences: A221466 A221467 A221468 * A221470 A221471 A221472

Keyword

nonn

Author

T. D. Noe, Jan 17 2013

Status

approved