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.

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

1,1

Comments

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

Links

Table of n, a(n) for n=1..100.

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.

Formula

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.

Mathematica

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]

Prog

(PARI) 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

Crossrefs

Cf. A232210, A257459, A257461.

Sequence in context: A081733 A102587 A272608 * A339471 A159834 A274576

Adjacent sequences: A257457 A257458 A257459 * A257461 A257462 A257463

Keyword

nonn,base

Author

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

Status

approved