This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A087403 #15 Jan 15 2015 19:23:05 %S A087403 11,2221,31,41,555555555551,61,71,881,991,101,1111111111111111111, %T A087403 1212121,131,14141414141,151,1616161,1717171717171717171717171717171, %U A087403 181,191,20201,211 %N A087403 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 A087403 Conjecture: No term is zero. %C A087403 Next term a(22) is too large (121 digits) to include in sequence. - _Ray Chandler_, Sep 23 2003 %C A087403 From _Farideh Firoozbakht_, Jan 07 2015: (Start) %C A087403 The conjecture is not true. There exist many numbers n such that a(n)=0. %C A087403 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 A087403 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 A087403 What is the smallest integer m, such that m > 1 and a(10^m) is nonzero? %C A087403 Conjecture: If n is not of the form 10^m then a(n) is nonzero. %C A087403 (End) %e A087403 a(2) = 2221 is a prime but 21 and 221 are composite. %Y A087403 Cf. A086766, A252491. %K A087403 base,nonn %O A087403 1,1 %A A087403 _Amarnath Murthy_, Sep 10 2003