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

1,5

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

Table of n, a(n) for n=1..86.

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.

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.

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

Cf. A257459, A232210, A257460.

Sequence in context: A031261 A188796 A161685 * A129398 A109009 A060904

Adjacent sequences: A257458 A257459 A257460 * A257462 A257463 A257464

Keyword

nonn,base

Author

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

Extensions

a(87) from Eric Chen, Apr 24 2015

Status

approved