Generalized Smarandache Palindromes

                          edited by George Gregory

     A Generalized Smarandache Palindrome is a number of the form:

     a₁a₂...a_na_n...a₂a₁  or  a₁a₂...a_n-1a_na_n-1...a₂a₁

     where all a₁, a₂, ..., a_n are positive integers of various number of digits.

    Examples:

     a)  1235656312 is a GSP because we can group it as (12)(3)(56)(56)(3)(12),

           i.e. ABCCBA.

b)      Of course, any integer can be consider a GSP because we may consider

the entire number as equal to a₁, which is smarandachely palindromic;

say N=176293 is GSP because we may take a₁ = 176293 and thus N=a₁.  

But one disregards this trivial case.

     Very interesting GSP are formed from smarandacheian sequences.

     Let's consider this one: 11, 1221, 123321, ..., 123456789987654321,

     1234567891010987654321, 12345678910111110987654321, ...

     all of them are GSP.

     It has been proven that 1234567891010987654321 is a prime

     (see http://www.kottke.org/notes/0103.html, and the Prime Curios site).

     A question:

     How many other GSP are in the above sequence?

Charles Ashbacher and Lori Neirynck proved that the density of GSP in the set of positive integers is approximatively 0.11.