Journal of Integer Sequences, Vol. 23 (2020), Article 20.7.3

Arithmetic Subderivatives: p-adic Discontinuity and Continuity

Pentti Haukkanen and Jorma K. Merikoski
Faculty of Information Technology and Communication Sciences
FI-33014 Tampere University

Timo Tossavainen
Department of Arts, Communication and Education
Lulea University of Technology
SE-97187 Lulea


In a previous paper, we proved that the arithmetic subderivative DS is discontinuous at any rational point with respect to the ordinary absolute value. In the present paper, we study this question with respect to the p-adic absolute value. In particular, we show that DS is in this sense continuous at the origin if S is finite or pS.

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(Concerned with sequences A000040 A003415.)

Received April 3 2020; revised version received June 24 2020. Published in Journal of Integer Sequences, June 26 2020.

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