Generalized Smarandache Palindromes
edited by George Gregory
A Generalized Smarandache Palindrome is a number of the form:
where all a1, a2, ..., an are positive
integers of various number of digits.
a) 1235656312 is a GSP
because we can group it as (12)(3)(56)(56)(3)(12),
Of course, any integer can be consider a GSP because we may consider
the entire number as equal to a1, which is smarandachely
say N=176293 is GSP because we may take a1 = 176293 and thus
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
and the Prime Curios site).
How many other GSP are in the above sequence?
Ashbacher and Lori Neirynck proved
that the density of GSP in the set of positive integers is approximatively 0.11.
proved that the density of GSP in the set of positive integers is approximatively 0.11.