A273846 - OEIS

%I #14 Mar 05 2020 22:27:55

%S 0,1,0,0,2,0,2,0,3,2,0,0,2,0,2,2,2,0,0,2,0,0,2,2,0,12,0,9,0,3,0,22,3,

%T 0,4,0,0,0,4,3,3,0,3,0,4,0,0,0,3,0,4,3,0,4,3,18,11,0,0,3,0,5,0,4,0,3,

%U 0,0,3,0,3,3,0,0,0,3,5,0,3,0,5,0,3,0

%N Smallest x > 0 such that 10^x - prime(n) is a prime number or 0 if no such prime exists.

%C For p(1) = 2, 10^x - 2 is divisible by 2 for all x > 0 so a(1) = 0.

%C For p(3) = 5, 10^x - 5 is divisible by 5 for all x > 0 so a(3) = 0.

%C For all prime(i) of the form 3*k+1, 10^x-prime(i) is divisible by 3 so a(i) = 0.

%C For n = 913, prime(n) = 7127, if x exists then x > 16000.

%H Pierre CAMI, <a href="/A273846/b273846.txt">Table of n, a(n) for n = 1..912</a>

%e 10^1 - 3 = 7 is prime, so a(2) = 1 as 3 = prime(2).

%e 10^1 - 11 is composite, 10^2 - 11 = 89 is prime, so a(5) = 2 as 11 = prime(5).

%o (PARI) a(n) = if((p=prime(n))%3==1 || n==1 || n==3, 0, for(x=1, oo, if(ispseudoprime(10^x-p), return(x)))); \\ _Jinyuan Wang_, Mar 05 2020

%K nonn

%O 1,5

%A _Pierre CAMI_, Jun 01 2016