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

Author

T. D. Noe, Jan 17 2013

Keywords

• nonn

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.

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.
		

Links

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

Crossrefs

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

Programs

Haskell

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

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}]