A294910 Numbers k such that (109*10^k + 17)/9 is prime.

2, 3, 9, 23, 27, 32, 50, 80, 107, 140, 992, 1607, 2975, 4007, 4605, 12392, 15159, 16628, 37419

Offset

1,1

Comments

For k > 1, numbers such that the digits 12 followed by k-1 occurrences of the digit 1 followed by the digit 3 is prime (see Example section).

a(20) > 2*10^5.

Links

Table of n, a(n) for n=1..19.

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

Makoto Kamada, Search for 121w3.

Example

2 is in this sequence because (109*10^2 + 17)/9 = 1213 is prime.
Initial terms and primes associated:
a(1) = 2, 1213;
a(2) = 3, 12113;
a(3) = 9, 12111111113;
a(4) = 23, 1211111111111111111111113;
a(5) = 27, 12111111111111111111111111113; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(109*10^# + 17)/9] &]

Crossrefs

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

Sequence in context: A057832 A089421 A151825 * A111240 A298407 A227252

Adjacent sequences: A294907 A294908 A294909 * A294911 A294912 A294913

Keyword

nonn,more,hard

Author

Robert Price, Nov 10 2017

Status

approved