Journal of Integer Sequences, Vol. 21 (2018), Article 18.8.4

About Some Relatives of the Taxicab Number

Viorel Niţică
Department of Mathematics
West Chester University of Pennsylvania
West Chester, PA 19383


The taxicab number, 1729, is the smallest number that can be written as a sum of two cubes in two different ways. It also has the following property: if we add its digits, we obtain 19. The number obtained from 19 by reversing the order of its digits is 91. If we multiply 19 by 91 we again obtain 1729. In the paper we study various generalizations of this property.

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(Concerned with sequences A005349 A067030 A305130 A305131.)

Received May 6 2018; revised versions received May 7 2018; May 13 2018; May 18 2018; May 19 2018; May 20 2018; July 10 2018; July 13 2018; October 15 2018. Published in Journal of Integer Sequences, December 9 2018.

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