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A242775 Let b_k=3...3 consist of k>=1 3's. Then a(n) is the smallest k such that the concatenation b_k and prime(n) is prime, or a(n)=0 if there is no such prime.

%I A242775 #20 Sep 23 2014 11:10:23
%S A242775 0,0,0,1,1,1,1,2,2,2,1,1,4,2,1,1,1,2,1,2,1,1,1,1,1,3,3,2,1,2,7,3,1,3,
%T A242775 2,2,8,1,1,7,2,1,1,5,3,2,2,2,3,1,3,8,5,1,1,4,3,1,4,5,3,6,1,2,1,2,1,3,
%U A242775 1,2,2,1,3,1,6,3,1,3,4,2,3,8,4,1,3,34,1
%N A242775 Let b_k=3...3 consist of k>=1 3's. Then a(n) is the smallest k such that the concatenation b_k and prime(n) is prime, or a(n)=0 if there is no such prime.
%C A242775 Conjecture: for n>=4, a(n)>0.
%C A242775 Records >=1: 1,2,4,7,8,34,... correspond to primes 7,19,41,127,157,443,...
%H A242775 Peter J. C. Moses, <a href="/A242775/b242775.txt">Table of n, a(n) for n = 1..2000</a>
%e A242775 For n<=3, a(n) = 0, because 3..32, 3..33 and 3..35 can never be prime, whatever the number of 3's that are concatenated.
%e A242775 For n=4, prime(n)=7, 37 is prime. So a(4)=1.
%o A242775 (PARI) a(n) = {if (n<=3, return (0)); p = prime(n); k = 1; while (! isprime(p = eval(concat("3", Str(p)))), k++); k; } \\ _Michel Marcus_, Sep 17 2014
%Y A242775 Cf. A232210, A247341, A247342.
%K A242775 nonn
%O A242775 1,8
%A A242775 _Vladimir Shevelev_, Sep 13 2014
%E A242775 More terms from _Peter J. C. Moses_, Sep 14 2014