Editing Thue–Morse sequence (section)

=== Direct definition ===
[[File:Thue-Morse binary digit sum.svg|thumb|128px|When counting in binary, the digit sum modulo 2 is the Thue–Morse sequence]]

To compute the ''n''th element ''t<sub>n</sub>'', write the number ''n'' in [[Binary number|binary]].  If the [[Hamming weight|number of ones]] in this binary expansion is odd then ''t<sub>n</sub>''&nbsp;=&nbsp;1, if even then ''t<sub>n</sub>''&nbsp;=&nbsp;0.<ref name=AS15>{{harvtxt|Allouche|Shallit|2003|p=15}}</ref>  That is, ''t<sub>n</sub>'' is the [[parity bit|even parity bit]] for ''n''. [[John H. Conway]] ''et al''. deemed numbers ''n'' satisfying ''t<sub>n</sub>''&nbsp;=&nbsp;1 to be ''odious'' (intended to be similar to ''odd'') numbers, and numbers for which ''t<sub>n</sub>''&nbsp;=&nbsp;0 to be ''evil'' (similar to ''even'') numbers.