Lots of numbers, plain and almost simple

Inder J. Taneja wants you to see some numbers, and so he presents them to you in this paper:

tanejaNatural Numbers from 44 to 1000 in terms of Increasing and Decreasing Orders of 1 to 9,” Inder J. Taneja, arXiv:1302.1479, February 6, 2013. The author [pictured here] was at one time a professor at the Universidade Federal de Santa Catarina, in Brazil, writes (using the royal We):

“In this work we have put the natural numbers starting from 44 to 1000 in terms of 1 to 9 in an increasing as well as decreasing orders. In both the cases some numbers are difficult to write, but from 71 onwards we have all. To bring these numbers, thousands of combinations are considered without use of any programming language. The next part of this work shall bring further numbers starting from 1001.”

Here are some of Inder J. Taneja’s many numbers:


The paper ends by saying:

Final Remarks: There are many ways to write each number. We have given preferences to one without use of brackets, except the numbers 247, 348, 337, 403, 604, 610, 622, 623, 695, 787, 788, 939, 940, 943, 954, 959, 991, 994, 997, 998, 999 and 1000 in the first case, and in the second case there are approximately 80 numbers where we have used the brackets. Since the work is done manually (without use of programming language), we are not sure whether it is possible the write these numbers without use of brackets. Any way, it is difficult to avoid brackets, because as numbers increases (1001 onwards) the possibilities of writing each number are very less. In the first case the numbers like, 1, 9, 10, 17, 18, 24, 25, 30, 31, 35, 36, 39, 40, 42 and 43 can also be written in the increasing order, but we have considered here from 44 onwards to have symmetry in both the cases. Unfortunately, the number 52 is not possible to write in both the situations.

References: This is first work of its kind, so there are no bibliographic references.

(Thanks to investigator Rodolfo Baggio for bringing this to our attention.)