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.

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

Offset: 1

Author

Vladimir Shevelev and Robert G. Wilson v, Apr 24 2015

Keywords

• nonn
• base

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

• Vladimir Shevelev and Robert G. Wilson v, Table of n, a(n) for n = 1..10000 with -1 for those entries where a(n) has not yet been found.

Crossrefs

Cf. A257459, A232210, A257460.

Programs

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]

Formula

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.

Extensions

a(87) from Eric Chen, Apr 24 2015