Various palindromic observations.
To start with... welcome to palindromic wonplate 121 !



Enoch Haga's observation from [ December 20, 2001 ]
"The vertical palindrome"
Starting with prime p = 103 up to 149 which are consecutive,
taking p and successively adding its digits to the next prime, we have

103 107 in  107 127 in  109 149 in  113 139 in  127 137 in  131 157 in  137 199 in  139 167 in  149 163 in	1 step 3 steps 5 3 1 3 5 3 1

a vertical palindromic sequence (unfortunately not prime) originates
1 3 5 3 1 3 5 3 1

I am confident that someone can find longer such palindromic sequences !

In the aftermath of the discovery of a new Mersenne Prime
Enoch observed that some of them have palindromic length.
See also Integer Sequence A028335

M1 has 1 digit
M2 has 1 digit
M3 has 2 digit
M4 has 3 digit
M5 has 4 digit
M6 has 6 digit
M7 has 6 digit
M11 has 33 digit
M18 has 969 digit

When will we have another palindromic number of digits ?
Alas not found in 2002...

Lastly Enoch noticed that M22 and M23 differ in length by 383 digits.
Yet another palindromic result!

Did You Know ?
Every Mersenne Number is a palindrome in base 2 (a binary repunit).