A257461 - OEIS

%I #13 May 03 2015 10:15:44

%S 1,0,1,1,5,1,1,1,1,2,28,1,1,1,1,2,1,1,4,1,1,3,1,2,90,1,1,2,8,2,1,1,2,

%T 1,1,2,1,4,6,8,3,2,3,4,1,1,5,1,5,60,1,1,5,6,1,2,1,1,2,1,10,1,1,1,5,2,

%U 1,3,4,1,1,2,4,1,3,4,3,2,1,1,2,1,6,1,5,3

%N Let b_k=9...9 consist of k>0 9's. Then a(n) is the smallest k such that the concatenation prime(n)b_k is prime, or a(n)=0 if there is no such prime.

%C The only unknown terms less than 10000, tested to 25000, are for n: 87, 5744, 8041, 9533.

%C For p(87)=449, the concatenation is divisible by 11 if k is odd and is divisible by 7 if k == 4 (mod 6).

%H Vladimir Shevelev and Robert G. Wilson v, <a href="/A257461/a257461_1.txt">Table of n, a(n) for n = 1..10000 with -1 for those entries where a(n) has not yet been found. </a>

%F a(n)=k for the least k such that p(n)*10^k+10^k-1 is prime, where p(n) is the n_th prime.

%t f[n_] := Block[{k = 1, p = Prime[n]}, While[ !PrimeQ[p*10^k + 10^k - 1], k++]; k]; f[2] = 0; Array[f, 86]

%Y Cf. A257459, A232210, A257460.

%K nonn,base

%O 1,5

%A _Vladimir Shevelev_ and _Robert G. Wilson v_, Apr 24 2015

%E a(87) from _Eric Chen_, Apr 24 2015