A280861 Numbers k such that (4*10^k + 83)/3 is prime.

0, 1, 3, 7, 9, 15, 17, 27, 37, 55, 58, 155, 228, 480, 720, 1305, 1573, 2173, 2547, 2767, 5448, 5500, 9468, 14268, 35207, 58155, 102612, 114340, 124420, 169559

Offset

1,3

Comments

For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 3 followed by the digits 61 is prime (see Example section).

a(31) > 2*10^5.

Links

Table of n, a(n) for n=1..30.

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

Makoto Kamada, Search for 13w61.

Example

3 is in this sequence because (4*10^3 + 83) / 3 = 1361 is prime.
Initial terms and associated primes:
a(1) = 0, 29;
a(2) = 1, 41;
a(3) = 3, 1361;
a(4) = 7, 13333361;
a(5) = 9, 1333333361; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(4*10^# + 83) / 3] &]

Crossrefs

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

Sequence in context: A210532 A110872 A032424 * A287264 A187108 A026175

Adjacent sequences: A280858 A280859 A280860 * A280862 A280863 A280864

Keyword

nonn,more,hard

Author

Robert Price, Jan 09 2017

Extensions

a(27)-a(30) from Robert Price, Feb 02 2018

Status

approved