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.

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

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) <= 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

Adjacent sequences: A078938 A078939 A078940 * A078942 A078943 A078944

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