**
Generalized
Smarandache Palindrome**

edited by George Gregory

A Generalized Smarandache Palindrome is a number of the form:

a_{1}a_{2}...a_{n}a_{n}...a_{2}a_{1
} or_{ } a_{1}a_{2}...a_{n-1}a_{n}a_{n-1..}.a_{2}a_{1}

where all a_{1}, a_{2}, ..., 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 a_{1}, which is smarandachely
palindromic;

say N=176293 is GSP because we may take a_{1} = 176293 and thus
N=a_{1}.

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