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A078941
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.
3
1, 4, 6, 8, 10, 12, 14, 15, 17, 18, 19, 21
OFFSET
1,2
COMMENTS
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.
REFERENCES
David S. Cohen and Manuel Blum, "On the problem of sorting burnt pancakes", Discrete Applied Math., 61 (1995) 105-120.
LINKS
J. Cibulka, Pancake Sorting [From D.J. Schreffler (dj_schreffler(AT)hotmail.com), Apr 17 2010]
Douglas B. West, The Pancake Problems (1975, 1979, 1973) - From N. J. A. Sloane, Jul 26 2012
FORMULA
a(n) >= A078942(n). a(n+1) <= a(n) + 2. 3n/2 <= a(n) <= 2n-2, where the upper bound holds for n>=10.
CROSSREFS
Cf. A078942. A058986 treats the unburnt case.
Sequence in context: A090334 A272601 A322368 * A078942 A248419 A186389
KEYWORD
nonn,more
AUTHOR
Dean Hickerson, Dec 18 2002
EXTENSIONS
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
STATUS
approved