A289081 Numbers k such that (4*10^k - 19)/3 is prime.

1, 2, 3, 4, 5, 8, 42, 52, 81, 96, 98, 152, 190, 261, 686, 1930, 2152, 5694, 6341, 14067, 18124, 31678, 58521, 73647, 128244

Offset

1,2

Comments

For k>1, numbers such that the digit 1 followed by k-2 occurrences of the digit 3 followed by the digits 27 is prime (see Example section).

a(26) > 2*10^5.

Links

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

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

Makoto Kamada, Search for 13w27.

Example

3 is in this sequence because (4*10^3 - 19)/3 = 1327 is prime.
Initial terms and primes associated:
a(1) = 1, 7;
a(2) = 2, 127;
a(3) = 3, 1327;
a(4) = 4, 13327;
a(5) = 5, 133327; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[(4*10^# - 19)/3] &]

Crossrefs

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

Sequence in context: A268274 A079383 A103670 * A105950 A227778 A371265

Adjacent sequences: A289078 A289079 A289080 * A289082 A289083 A289084

Keyword

nonn,more,hard

Author

Robert Price, Jun 23 2017

Extensions

a(25) from Robert Price, Mar 01 2018

Status

approved