

A257461


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.


3



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, 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, 1, 3, 4, 1, 1, 2, 4, 1, 3, 4, 3, 2, 1, 1, 2, 1, 6, 1, 5, 3
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OFFSET

1,5


COMMENTS

The only unknown terms less than 10000, tested to 25000, are for n: 87, 5744, 8041, 9533.
For p(87)=449, the concatenation is divisible by 11 if k is odd and is divisible by 7 if k == 4 (mod 6).


LINKS



FORMULA

a(n)=k for the least k such that p(n)*10^k+10^k1 is prime, where p(n) is the n_th prime.


MATHEMATICA

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


CROSSREFS



KEYWORD

nonn,base


AUTHOR



EXTENSIONS



STATUS

approved



