A078942 Flipping burnt pancakes. Given a sorted stack of n burnt pancakes of different sizes (smallest on top, ..., largest at the bottom), each with its burnt side up, a(n) is the number of spatula flips needed to restore them to their initial order but with the burnt sides down.

1, 4, 6, 8, 10, 12, 14, 15, 17, 18, 19, 21, 22, 23, 24, 26, 28, 29

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 this initial configuration is a worst case for the general problem of sorting burnt pancakes. If so, then this sequence is identical to A078941.

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..18.

Douglas B. West, The Pancake Problems (1975, 1979, 1973) - From N. J. A. Sloane, Jul 26 2012

Formula

a(n) <= A078941(n). a(n+1) <= a(n) + 2. 3n/2 <= a(n) <= 47n/30 + c for some constant c.

Crossrefs

Cf. A078941, A058986.

Sequence in context: A272601 A322368 A078941 * A248419 A186389 A039767

Adjacent sequences: A078939 A078940 A078941 * A078943 A078944 A078945

Keyword

nonn,more

Author

Dean Hickerson, Dec 18 2002

Status

approved