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A221469
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Number of increasing peak values in the Collatz (3x+1) iteration of n.
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4
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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
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OFFSET
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1,3
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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}]
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PROG
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(Haskell)
a221469 n = sum $ map fromEnum $ zipWith (>) (tail ts) ts where
ts = scanl1 max $ a070165_row n
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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