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


WELCOME TO 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).


A000121 Prime Curios! Prime Puzzle
Wikipedia 121 Le nombre 121














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Patrick De Geest - Belgium - Short Bio - Some Pictures
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