1001, a Scheherazade palindrome !
1001 is the twenty-sixth pentagonal number ! 26*(3*26-1)/2 (Sloane's A000326)
1001 is the fourth palindromic pentagonal number.
See Sloane's A002069 : 1 , 5 , 22 , 1001 , ...
1001 is the product of three consecutive primes : 7 * 11 * 13
A nice finite pattern can be made with 1001
10011 = 1001
10012 = 1002001
10013 = 1003003001
10014 = 1004006004001
The following property of 1001 was discovered by [G. L. Honaker, Jr.]
General formulation : Prime p * Sum of the next p consecutive primes = a palindrome.
[ Dropping the palindrome condition gives sequence A036660. ]
1001 = 7 * (11+13+17+19+23+29+31) [Prime Curios!]
There exist a second palindrome with this property namely 3883
3883 = 11 * (13+17+19+23+29+31+37+41+43+47+53) [Prime Curios!]
Both the prime and the sum of primes of this last solution are palindromic primes !
3883 = 11 * (353)
Who can find the third palindromic solution ?
The largest (probable) prime of 326, 3191, 3419, etc. digits is made with
1001 as the negative displacement from those power of ten axes
10326 – 1001
103191 – 1001
103419 – 1001
103546 – 1001
107866 – 1001
1012189 – 1001
1012687 – 1001
1015132 – 1001
1015167 – 1001
1016366 – 1001
1018138 – 1001
A000031 