cp's OEIS Frontend

A087606 Smallest k such that n times concatenation of k with itself followed by a 9 is a prime, or 0 if no such number exists.

%I A087606 #7 Dec 05 2013 19:56:32
%S A087606 1,2,0,1,1,0,1,11,0,64,5,0,2,31,0,1,5,0,10,65,0,41,212,0,5,79,0,41,
%T A087606 160,0,5,94,0,8,82,0,23,43,0,40,26,0,391,119,0,212,4,0,1,160,0,134,28,
%U A087606 0,208,50,0,248,35,0,113,43,0,79,7,0,70,170,0,64,94,0,19,86,0,10,118,0,34,98
%N A087606 Smallest k such that n times concatenation of k with itself followed by a 9 is a prime, or 0 if no such number exists.
%C A087606 Conjecture: a(3n) = 0. No other term is zero.
%C A087606 a(3n)=0: consider the sum of the digits modulo 3. For the same reason, if a(m) is divisible by 3 then a(m)=0. - _Sam Alexander_, Nov 15 2003
%H A087606 XIAO Gang, <a href="http://wims.unice.fr/wims/wims.cgi">Factoris - a program that factorizes huge integers</a>, 1997-1999
%e A087606 a(2) = 2 as 229 is a prime. but 119 is not.
%t A087606 s[b_]:=(v={};l=Length[b];Do[v=Join[v, IntegerDigits[b[[k]]]], {k, l}];v); a[n_]:=If[Mod[n, 3]!= 0, (For[m = 1, ! PrimeQ[10*FromDigits[s[Table[m, {n}]]] +9], m++ ];m), 0]; Table[a[n], {n, 90}] (Firoozbakht)
%Y A087606 Cf. A086920, A087604, A087605, A087607, A087608, A087609, A087610.
%K A087606 base,nonn
%O A087606 1,2
%A A087606 _Amarnath Murthy_, Sep 18 2003
%E A087606 More terms from _Sam Alexander_, Nov 15 2003
%E A087606 More terms from _Farideh Firoozbakht_, Feb 04 2005