Journal of Integer Sequences, Vol. 6 (2003), Article 03.3.4

How to Differentiate a Number

Victor Ufnarovski

Centre for Mathematical Sciences

Lund Institute of Technology

P.O. Box 118

SE-221 00 Lund

Sweden



Bo Åhlander

KTH/2IT

Electrum 213

164 40 Kista

Sweden



Abstract:

We define the derivative of an integer to be the map sending every prime to 1 and satisfying the Leibnitz rule. The aim of the article is to consider the basic properties of this map and to show how to generalize the notion to the case of rational and arbitrary real numbers. We make some conjectures and find some connections with Goldbach's Conjecture and the Twin Prime Conjecture. Finally, we solve the easiest associated differential equations and calculate the generating function.

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(Concerned with sequence A003415 .)

Received April 4, 2003; revised version received July 27, 2003. Published in Journal of Integer Sequences September 17, 2003.