On Smarandache Generalized Palindrome
by
Chong Hu
University of Seoul, Korea
Coauthors: Charles Ashbacher

A Smarandache Generalized Palindrome has one of the forms: a(1)a(2)...a(n-1)a(n)a(n-1)...a(2)a(1) or a(1)a(2)...a(n-1)a(n)a(n)a(n-1)...a(2)a(1), where all a(k) are positive integers of one or more digits, and all above a(k) integers are concatenated. (When all a(k) integers have a digit only, one gets the classical definition of the palindrome.) Obviously, when n=1 in the first case, one can consider any positive integer as a SGP because, say 1743902 = (1743902), i.e. a(1) = 1743902. But let's take in the first case n > 1. Examples of SGP: 1457567145 because 1457567145 = (145)(7)(56)(7)(145), also 145756567145 because 145756567145 = (145)(7)(56)(56)(7)(145). Question: how many terms from the Smarandache cubic complement sequence (i.e., for each integer n to find the smallest integer k such that nk is a perfect cub): 1,4,9,2,25,36,49,1,3,100,121,18,169,196,225,4,289,12,361,50,441,484,529,9,5,676,1,841,900,961,2,1089,1156,1225,6,1369,1444,1521,25,1681,1764,1849,...) are SGP (of course n>1)? Reference: F.Smarandache, Properties of numbers, University of Craiova, 1972.

Date received: November 28, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caft-25.