A087403 - OEIS

%I #15 Jan 15 2015 19:23:05

%S 11,2221,31,41,555555555551,61,71,881,991,101,1111111111111111111,

%T 1212121,131,14141414141,151,1616161,1717171717171717171717171717171,

%U 181,191,20201,211

%N a(n) = smallest prime of the form 10*K(n) + 1, where K is a number obtained by concatenation of n with itself, or 0 if no such prime exists.

%C Conjecture: No term is zero.

%C Next term a(22) is too large (121 digits) to include in sequence. - _Ray Chandler_, Sep 23 2003

%C From _Farideh Firoozbakht_, Jan 07 2015: (Start)

%C The conjecture is not true. There exist many numbers n such that a(n)=0.

%C By using the theorem and its corollary mentioned in the comments lines of the sequence A086766, we can prove that for m = 2, 3, ..., 275 a(10^m)=0.

%C What is the smallest odd prime p, such that (10^(p^2)-1)/(10^p-1) is a prime number (a(10^(p-1)) is nonzero)?

%C What is the smallest integer m, such that m > 1 and a(10^m) is nonzero?

%C Conjecture: If n is not of the form 10^m then a(n) is nonzero.

%C (End)

%e a(2) = 2221 is a prime but 21 and 221 are composite.

%Y Cf. A086766, A252491.

%K base,nonn

%O 1,1

%A _Amarnath Murthy_, Sep 10 2003