A282456 Numbers k such that 18*10^k + 1 is prime.

0, 1, 2, 4, 9, 12, 21, 55, 307, 332, 388, 820, 1593, 2432, 2438, 3372, 6270, 7437, 8268, 12135, 16588, 41397, 46126, 47910, 81091

Offset

1,3

Comments

For k>0, numbers such that the digits 18 followed by k-1 occurrences of the digit 0 followed by the digit 1 is prime (see Example section).

a(26) > 10^5.

Links

Table of n, a(n) for n=1..25.

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

Makoto Kamada, Search for 180w1.

Example

2 is in this sequence because 18*10^2 + 1 = 1801 is prime.
Initial terms and primes associated:
a(1) = 0, 19;
a(2) = 1, 181;
a(3) = 2, 1801;
a(4) = 4, 180001;
a(5) = 9, 18000000001; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[18*10^# + 1] &]

Crossrefs

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

Sequence in context: A241200 A092530 A154891 * A176472 A139557 A103690

Adjacent sequences: A282453 A282454 A282455 * A282457 A282458 A282459

Keyword

nonn,more,hard

Author

Robert Price, Feb 15 2017

Status

approved