cp's OEIS Frontend

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.

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.

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%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