

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
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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) 105120.


LINKS

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


FORMULA

a(n) >= A078942(n). a(n+1) <= a(n) + 2. 3n/2 <= a(n) <= 2n2, where the upper bound holds for n>=10.


CROSSREFS

Cf. A078942. A058986 treats the unburnt case.
Sequence in context: A228358 A134331 A090334 * A078942 A186389 A039767
Adjacent sequences: A078938 A078939 A078940 * A078942 A078943 A078944


KEYWORD

nonn,more


AUTHOR

Dean Hickerson (dean.hickerson(AT)yahoo.com), 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



