

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_{n1}a_{n}a_{n1..}.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 