Subsequences of automatic sequences indexed by<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mo stretchy="false">⌊</mml:mo><mml:msup><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msup><mml:mo stretchy="false">⌋</mml:mo></mml:math>and correlations

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