A294126 Numbers k such that (44*10^k - 791)/9 is prime.

2, 3, 9, 15, 20, 23, 63, 66, 75, 93, 120, 480, 504, 812, 872, 1124, 3888, 9882, 14859, 33786, 44736, 83768

Offset

1,1

Comments

For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 8 followed by the digits 01 is prime (see Example section).

a(23) > 2*10^5.

Links

Table of n, a(n) for n=1..22.

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

Makoto Kamada, Search for 48w01.

Example

2 is in this sequence because (44*10^2 - 791)/9 = 401 is prime.
Initial terms and associated primes:
a(1) = 2, 401;
a(2) = 3, 4801;
a(3) = 9, 4888888801;
a(4) = 15, 4888888888888801;
a(5) = 20, 488888888888888888801; etc.

Mathematica

Select[Range[2, 100000], PrimeQ[(44*10^# - 791)/9] &]

Prog

(Magma) [n: n in [1..400] |IsPrime((44*10^n - 791) div 9)]; // Vincenzo Librandi, Dec 03 2018

Crossrefs

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

Sequence in context: A108825 A109663 A056702 * A091361 A092352 A061933

Adjacent sequences: A294123 A294124 A294125 * A294127 A294128 A294129

Keyword

nonn,more,hard

Author

Robert Price, Oct 23 2017

Status

approved