cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A239091 Prefix overlap of dictionary consisting of binary expansions of 0 through n.

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%I A239091 #21 Jul 17 2025 19:25:03
%S A239091 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 A239091 59,63,65,69,72,76,77,82,86,91,94,99,103,108,110,115,119,124,127,132,
%U A239091 136,141,142,147,151,156,159,164,168,173,175,180,184,189,192,197,201,206
%N A239091 Prefix overlap of dictionary consisting of binary expansions of 0 through n.
%C A239091 The prefix overlap of a dictionary is the sum of the prefix overlaps between successive words.
%C A239091 Partial sums of A238845.
%H A239091 Alois P. Heinz, <a href="/A239091/b239091.txt">Table of n, a(n) for n = 1..10000</a>
%H A239091 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.
%F A239091 a(n) = A061168(n+1) - A011371(n+1) + A000523(n+1). - _Alan Michael Gómez Calderón_, Jul 17 2025
%e A239091 For n=5 the dictionary is
%e A239091 0
%e A239091 1
%e A239091 10
%e A239091 11
%e A239091 100
%e A239091 101
%e A239091 and the successive prefix overlaps are 0,1,1,1,2, whose sum is a(5)=5.
%Y A239091 Cf. A000523, A011371, A061168, A238845, A239092.
%K A239091 nonn,base
%O A239091 1,3
%A A239091 _N. J. A. Sloane_, Mar 22 2014