Consider the series of semiprimes. Now consider the series of numbers representing the Sum Of Digits (SOD) of each semiprime.

(1.) How many times does the number '9' occur, and why?

(2.) What is the smallest semiprime that has the same SOD as the next consecutive semiprime? or prove that there is no pair of consecutive semiprimes that have the same SOD.

(1) If the SOD of digits of an integer, A, is 9, then A must be divisible by 9. It follows that the only semiprime whose SOD = 9 is 9 itself.

Edited on September 8, 2009, 12:49 pm

Posted by FrankM on 2009-09-08 12:48:24