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

Author

Dean Hickerson, Dec 18 2002

Keywords

• nonn
• more

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

Crossrefs

Cf. A078942. A058986 treats the unburnt case.

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.

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