WON TOPIC 121

World!Of
Numbers

WON plate
121 |

[ December 20, 2001 ]
Various palindromic observations
To start with... welcome to palindromic WONplate 121 !
Enoch Haga

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

[ TOP OF PAGE]