A242775 Let b_k=3...3 consist of k>=1 3's. Then a(n) is the smallest k such that the concatenation b_k and prime(n) is prime, or a(n)=0 if there is no such prime.

0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 1, 1, 4, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 3, 3, 2, 1, 2, 7, 3, 1, 3, 2, 2, 8, 1, 1, 7, 2, 1, 1, 5, 3, 2, 2, 2, 3, 1, 3, 8, 5, 1, 1, 4, 3, 1, 4, 5, 3, 6, 1, 2, 1, 2, 1, 3, 1, 2, 2, 1, 3, 1, 6, 3, 1, 3, 4, 2, 3, 8, 4, 1, 3, 34, 1

Offset

1,8

Comments

Conjecture: for n>=4, a(n)>0.

Records >=1: 1,2,4,7,8,34,... correspond to primes 7,19,41,127,157,443,...

Links

Peter J. C. Moses, Table of n, a(n) for n = 1..2000

Example

For n<=3, a(n) = 0, because 3..32, 3..33 and 3..35 can never be prime, whatever the number of 3's that are concatenated.
For n=4, prime(n)=7, 37 is prime. So a(4)=1.

Prog

(PARI) a(n) = {if (n<=3, return (0)); p = prime(n); k = 1; while (! isprime(p = eval(concat("3", Str(p)))), k++); k; } \\ Michel Marcus, Sep 17 2014

Crossrefs

Cf. A232210, A247341, A247342.

Sequence in context: A089722 A172356 A184948 * A079562 A338664 A199803

Adjacent sequences: A242772 A242773 A242774 * A242776 A242777 A242778

Keyword

nonn

Author

Vladimir Shevelev, Sep 13 2014

Extensions

More terms from Peter J. C. Moses, Sep 14 2014

Status

approved