Geodesic
How to differentiate a number
Journal of integer sequences, Tome 6 (2003) no. 3.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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. Full version: pdf, dvi, ps, latex
Classification : 11A25, 11A41, 11N05, 11N56, 11Y55
Keywords: arithmetic derivative, goldbach's conjecture, the twin prime conjecture, prime numbers, leibnitz rule, integer sequence, generating function 
@article{JIS_2003__6_3_a2,
     author = {Ufnarovski, Victor and \r{A}hlander, Bo},
     title = {How to differentiate a number},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
     volume = {6},
     number = {3},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2003__6_3_a2/}
}
TY  - JOUR
AU  - Ufnarovski, Victor
AU  - Åhlander, Bo
TI  - How to differentiate a number
JO  - Journal of integer sequences
PY  - 2003
VL  - 6
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JIS_2003__6_3_a2/
LA  - en
ID  - JIS_2003__6_3_a2
ER  - 
%0 Journal Article
%A Ufnarovski, Victor
%A Åhlander, Bo
%T How to differentiate a number
%J Journal of integer sequences
%D 2003
%V 6
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JIS_2003__6_3_a2/
%G en
%F JIS_2003__6_3_a2
Ufnarovski, Victor; Åhlander, Bo. How to differentiate a number. Journal of integer sequences, Tome 6 (2003) no. 3. http://geodesic.mathdoc.fr/item/JIS_2003__6_3_a2/