

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.


2



1, 4, 6, 8, 10, 12, 14, 15, 17, 18, 19, 21, 22, 23, 24, 26, 28, 29
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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 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) 105120.


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



