Here's what Math Reviews has to say:
AUTHOR(S): Gates, William H.
Papadimitriou, Christos H.
TITLE: Bounds for sorting by prefix reversal.
SOURCE: Discrete Mathematics
27 (1979), no. 1, 47--57.
REVIEW: The authors study the problem of sorting a sequence of
distinct numbers by prefix reversal -- reversing a
subsequence of adjacent numbers which always contains the
first number of the current sequence. Let f(n) denote the
smallest number of prefix reversals which is sufficient to
sort n numbers in any ordering. The authors prove that f(n)
<= (5n+5)/3 by demonstrating an algorithm which never needs
more prefix reversals. They also prove that f(n) >= 17n/16
whenever n is a multiple of 16. The sequences which achieve
this bound are periodic extensions of the basic sequence 1,
7, 5, 3, 6, 4, 2, 8, 16, 10, 12, 14, 11, 13, 15, 9. If,
furthermore, each integer is required to participate in an
even number of prefix reversals, the corresponding function
g(n) is shown to satisfy 3n/2 - 1 <= g(n) <= 2n+3.
REVIEWER: Hwang, Frank K.
(Murray Hill, N.J.)