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A078941
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Flipping burnt pancakes. Maximum number of spatula flips to sort a stack of n pancakes of different sizes, each burnt on one side, so that the smallest ends up on top, ..., the largest at the bottom and each has its burnt side down.
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3
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1, 4, 6, 8, 10, 12, 14, 15, 17, 18, 19, 21
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OFFSET
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1,2
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COMMENTS
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In a 'spatula flip', a spatula is inserted below any pancake and all pancakes above the spatula are lifted and replaced in reverse order.
It is conjectured that the initial configuration in which the pancakes are in the correct order but all of the burnt sides are up is a worst case for the problem. If so, then this sequence is identical to A078942.
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REFERENCES
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David S. Cohen and Manuel Blum, "On the problem of sorting burnt pancakes", Discrete Applied Math., 61 (1995) 105-120.
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LINKS
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J. Cibulka, Pancake Sorting [From D.J. Schreffler (dj_schreffler(AT)hotmail.com), Apr 17 2010]
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FORMULA
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a(n) >= A078942(n). a(n+1) <= a(n) + 2. 3n/2 <= a(n) <= 2n-2, where the upper bound holds for n>=10.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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Two new terms added from a 2009 presentation. See the University of Montreal link below. D.J. Schreffler (dj_schreffler(AT)hotmail.com), Apr 17 2010
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STATUS
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approved
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