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Prefix overlap of dictionary consisting of binary expansions of 0 through n.
2

%I #14 Mar 20 2019 04:24:20

%S 0,1,2,3,5,6,8,9,12,14,17,18,21,23,26,27,31,34,38,40,44,47,51,52,56,

%T 59,63,65,69,72,76,77,82,86,91,94,99,103,108,110,115,119,124,127,132,

%U 136,141,142,147,151,156,159,164,168,173,175,180,184,189,192,197,201,206

%N Prefix overlap of dictionary consisting of binary expansions of 0 through n.

%C The prefix overlap of a dictionary is the sum of the prefix overlaps between successive words.

%C Partial sums of A238845.

%H Rodica Simion and Herbert S. Wilf, <a href="https://doi.org/10.1137/0607054">The distribution of prefix overlap in consecutive dictionary entries</a>, SIAM J. Algebraic Discrete Methods, 7(1986), no. 3, 470--475. MR0844051.

%e For n=5 the dictionary is

%e 0

%e 1

%e 10

%e 11

%e 100

%e 101

%e and the successive prefix overlaps are 0,1,1,1,2, whose sum is a(5)=5.

%Y Cf. A238845, A239092.

%K nonn,base

%O 1,3

%A _N. J. A. Sloane_, Mar 22 2014