A213883 Least number k such that (10^k-j)*10^n-1 is prime for some single-digit j or 0 if no such prime with 1<=k, 0<=j<=9 exists.

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 2, 1, 1, 3, 5, 5, 3, 1, 3, 3, 1, 1, 9, 1, 1, 1, 1, 1, 7, 3, 6, 4, 1, 4, 4, 1, 15, 10, 1, 7, 3, 1, 3, 2, 2, 4, 6, 1, 3, 5, 20, 1, 1, 1, 8, 10, 7, 15, 10, 1, 4, 2, 5, 8, 3, 23, 11, 2, 2, 9, 3, 1, 5, 4, 1, 6, 3, 18, 2

Offset: 1

Author

Pierre CAMI, Jun 26 2012

Keywords

• nonn

Comments

j cannot be 0, 3, 6 or 9 because we are searching for repdigit primes with k-1 times the digit 9, one digit (9-j), and n least-significant digits 9 (so n+k-1 times the digit 9 in total). If j is a multiple of 3, that number is also a multiple of 3 and not prime.

Conjecture: there is always at least one (k,j) solution for each n.

Examples

			Refers to the primes 89, 599, 8999, 79999, 799999, 4999999, 89999999,...
		

Links

• Pierre CAMI, Table of n, a(n) for n = 1..2200

Crossrefs

Cf. A213790, A213884 (corresponding j).

Programs

Maple

A213883 := proc(n)
    for k from 1 to 2*n-1 do
        for j from 0 to 9 do
            if isprime( (10^k-j)*10^n-1) then
                return k;
            end if;
        end do:
    end do:
    return 0 ;
end proc: # R. J. Mathar, Jul 20 2012