A289050 Numbers k such that (91*10^k + 17)/9 is prime.

1, 2, 4, 7, 14, 19, 20, 53, 62, 65, 68, 130, 170, 358, 449, 595, 703, 1502, 2192, 8582, 31573, 39839, 45022

Offset

1,2

Comments

For k>0, numbers such that the digits 10 followed by k-1 occurrences of the digit 1 followed by the digit 3 is prime (see Example section).

a(24) > 2*10^5.

Links

Table of n, a(n) for n=1..23.

Makoto Kamada, Factorization of near-repdigit-related numbers.

Makoto Kamada, Search for 101w3.

Example

4 is in this sequence because (91*10^4 + 17)/9 = 101113 is prime.
Initial terms and primes associated:
a(1) = 1, 103;
a(2) = 2, 1013;
a(3) = 4, 101113;
a(4) = 7, 101111113;
a(5) = 14, 1011111111111113; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(91*10^# + 17)/9] &]

Crossrefs

Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

Sequence in context: A018476 A265309 A293825 * A133638 A367266 A018505

Adjacent sequences: A289047 A289048 A289049 * A289051 A289052 A289053

Keyword

nonn,more,hard

Author

Robert Price, Jun 22 2017

Status

approved