shadow nacelle
Number 11.
N I got as 1+10²+10³....10^2(n-1) where n is the number of 1 in N. I have got the pattern as( 10^n+1)(10^n -1) /99 . how do I prove it is not prime except n=2. I tried but I got some repetitive patterns. because we know that 10^n-1 divides 99 if n->even. (proof by induction )if n is odd 10^n -1 gives 9 factor and 10^n+1 gives 11 factor. but trouble proving composite. . for even cases for example n=4. I am getting 10001 × 101 . 101 is n=2. for n=6. 1000001 × 10101 . 10101 is n=3 . for n=8 i am getting 100000001× 1010101. 1010101 is for n=4. so for n=2n. N(2n)= 100....1 × N(n). so maybe I can use some induction here. but that would be for only even n. Now for n= odd I am getting 9090...91 × 111....1111 . where 11...111 are repunites with n number of 1 . and it is not always composite for example 19 1s and 23 1s ( I can't prove , i just check in a program) . Sorry if I explained badly . Help is appreciated
sullen kiln
real escarp