A293272 Numbers k such that (10^k - 19)/9 is prime.

3, 4, 6, 9, 34, 36, 126, 141, 160, 286, 678, 1236, 3757, 4681, 4881, 6360, 6588, 7056, 7752, 41925, 43423, 43503, 47565, 52608, 55084, 76069, 199248

Offset

1,1

Comments

For k > 1, numbers such that k-2 occurrences of the digit 1 followed by the digits 09 is prime (see Example section).

a(28) > 2*10^5.

Links

Table of n, a(n) for n=1..27.

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

Makoto Kamada, Search for 1w09

Example

4 is in this sequence because (10^4 - 19)/9 = 1109 is prime.
Initial terms and primes associated:
a(1) = 3, 109;
a(2) = 4, 1109;
a(3) = 6, 111109;
a(4) = 9, 111111109;
a(5) = 34, 1111111111111111111111111111111109; etc.

Mathematica

Select[Range[2, 100000], PrimeQ[10^# - 19)/9] &]

Crossrefs

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

Sequence in context: A338061 A350741 A191699 * A192286 A242028 A254002

Adjacent sequences: A293269 A293270 A293271 * A293273 A293274 A293275

Keyword

nonn,more,hard

Author

Robert Price, Oct 06 2017

Extensions

a(27) from Robert Price, Jan 02 2018

Status

approved