generalized Smarandache palindrome
Find the number of GSP of four digits that are not palindromic numbers in base 10.
M. Khoshnevisan, Griffith University, Gold Coast, Queensland 9726, Australia.
Before solving the problem, let see some examples:
1) 1235656312 is a GSP because we can group it as (12)(3)(56)(56)(3)(12), i.e. ABCCBA.
2) The number 5675 is also a GSP because it can be written as (5)(67)(5).
3) Obviously, any palindromic number is a GSP number as well.
A palindromic number of four digits has the concatenated form: abba, where and . There are palindromic numbers of four digits. For example, 1551, or 2002 are palindromic (and, of course, GSP too); yet 3753 is not palindromic but it is a GSP for 3753=3(75)3, i.e. of the form ABA; similarly 4646, for it can be organized as (46)(46), i.e. of the form CC. Therefore, a SGP, different from a palindromic number, should have the concatenated forms: 1) ABA, where and ; 2) or CC, where . In the first case, one has . In the second case, one has . Total: GSP numbers of four digits which are not palindromic.
1. Charles Ashbacher, Lori Neirynck, www.gallup.unm.edu/ smarandache/GeneralizedPalindromes.htmThe Density of Generalized Smarandache Palindromes, Journal of Recreational Mathematics, Vol. 33 (2), 2006
2. G. Gregory, http://www.gallup.unm.edu/ smarandache/GSP.htmGeneralized Smarandache Palindromes
3. M. Khoshnevisan, ”Generalized Smarandache Palindrome”, Mathematics Magazine, Aurora, Canada, 10/2003.
4. M. Khoshnevisan, Proposed Problem 1062 (on Generalized Smarandache Palindrome), The ME Epsilon, USA, Vol. 11, No. 9, p. 501, Fall 2003.
5. Mark Evans, Mike Pinter, Carl Libis, Solutions to Problem 1062 (on Generalized Smarandache Palindrome), The ME Epsilon, Vol. 12, No. 1, 54-55, Fall 2004.
7. F. Smarandache, http://www.gallup.unm.edu/ smarandache/Sequences-book.pdfSequences of Numbers Involved in Unsolved Problems, Hexis, 1990, 2006
|Title||generalized Smarandache palindrome|
|Date of creation||2013-03-22 17:03:25|
|Last modified on||2013-03-22 17:03:25|
|Last modified by||dankomed (17058)|