A257461 -id:A257461 - cp's OEIS frontend

A257459 Let b_k=1...1 consist of k>0 1'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.

2, 1, 5, 1, 17, 1, 8, 1, 2, 6, 1, 0, 2, 1, 3, 9, 18, 4, 210, 6, 7, 3, 2, 6, 1, 2, 1, 2, 1, 2, 4, 3, 2, 24, 3, 1, 1, 6, 5, 11, 2, 1, 11, 1, 12, 6, 1, 7, 3, 39, 2, 2, 1, 2, 9, 3, 5, 1, 6, 2, 3, 2, 180, 3, 15, 17, 24, 1, 5, 1, 2, 2, 1, 64, 7, 6, 3, 24, 2, 1, 2, 1, 6, 16, 1, 9, 8, 6, 17, 4, 6, 2, 1, 9, 30, 2, 6, 44, 1, 6

Offset: 1

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

The only unknown terms less than 10000, tested to 15000, are for n: 284, 714, 1257, 1618, 2248, 2450, 2779, 3886, 3891, 4007, 4359, 4784, 4912, 5364, 6108, 6356, 6371, 7570, 7668, 8446, 9606.

Prime(12)=37 and b_k for k == 2 (mod 3), the concatenation is divisible by 3; for k == 1 (mod 3), the concatenation is divisible by either 7 or 13; and finally for k == 0 (mod 3), the concatenation is divisible by 37.

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.

Cf. A232210, A257460, A257461.

f[n_] := Block[{k = 1, p = Prime[n]}, While[ !PrimeQ[p*10^k + (10^k - 1)/9], k++]; k]; f[12] = 0; Array[f, 100]

a(n)=k for the least k such that p(n)*10^k+(10^k-1)/9 is prime, where p(n) is the n_th prime.

A257460 Let b_k=7...7 consist of k>0 7'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.

Original entry on oeis.org

2, 1, 2, 0, 3, 1, 2, 1, 2, 48, 1, 10, 2, 3, 3, 3, 9, 1, 1, 2, 66, 1, 2, 8, 1, 2, 6, 3, 1, 3, 1, 2, 3, 6, 8, 9, 7, 1, 3, 2, 2, 3, 17, 4, 2, 1, 3, 1, 2, 1, 3, 2, 1, 5, 17, 5, 8, 16, 1, 3, 1, 8, 6, 2, 1, 3, 3, 2184, 6, 6, 3, 2, 1, 3, 1, 2, 2, 4, 2, 3, 3, 1, 2, 1, 1, 3, 6, 15, 5, 1, 48, 2, 1, 2, 7, 2, 47, 2, 1, 1

Offset: 1

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

The only unknown terms less than 10000, tested to 17500, are for n: 484, 1291, 2096, 2238, 3503, 3859, 6674, 7087, 7824, 8954.

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

Cf. A232210, A257459, A257461.

f[n_] := Block[{k = 1, p = Prime[n]}, While[ !PrimeQ[p*10^k + 7(10^k - 1)/9], k++]; k]; f[4] = 0; Array[f, 100]

isok(k, dp) = ispseudoprime(fromdigits(concat(dp, vector(k, i, 7))));
a(n) = {if (prime(n) == 7, return(0)); my(k=1, p=prime(n)); while (!ispseudoprime(p*10^k+7*(10^k-1)/9), k++); k;} \\ Michel Marcus, Jan 20 2021

a(n)=k for the least k such that prime(n)*10^k+7*(10^k-1)/9 is prime, where prime(n) is the n-th prime.

cp's OEIS Frontend

A257459 Let b_k=1...1 consist of k>0 1'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.

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