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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 (list; graph; refs; listen; history; text; internal format)



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.


David S. Cohen and Manuel Blum, "On the problem of sorting burnt pancakes", Discrete Applied Math., 61 (1995) 105-120.


Table of n, a(n) for n=1..12.

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


a(n) >= A078942(n). a(n+1) <= a(n) + 2. 3n/2 <= a(n) <= 2n-2, where the upper bound holds for n>=10.


Cf. A078942. A058986 treats the unburnt case.

Sequence in context: A228358 A134331 A090334 * A078942 A248419 A186389

Adjacent sequences:  A078938 A078939 A078940 * A078942 A078943 A078944




Dean Hickerson, Dec 18 2002


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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Last modified November 27 14:07 EST 2015. Contains 264550 sequences.