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 ?
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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
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