A294124 Numbers k such that (13*10^k + 179)/3 is prime.

1, 5, 8, 21, 37, 61, 62, 126, 188, 221, 253, 523, 654, 1875, 2372, 2394, 3073, 4158, 6663, 6881, 167911

Offset

1,2

Comments

For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 3 followed by the digits 93 is prime (see Example section).

a(22) > 2*10^5.

Links

Table of n, a(n) for n=1..21.

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

Makoto Kamada, Search for 43w93.

Example

5 is in this sequence because (13*10^5 + 179)/3 = 433393 is prime.
Initial terms and associated primes:
a(1) = 1, 103;
a(2) = 5, 433393;
a(3) = 8, 433333393;
a(4) = 21, 4333333333333333333393;
a(5) = 37, 43333333333333333333333333333333333393; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(13*10^# + 179)/3] &] (* corrected by Georg Fischer, Jul 22 2019 *)

Crossrefs

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

Sequence in context: A138810 A331700 A105634 * A120036 A036381 A363224

Adjacent sequences: A294121 A294122 A294123 * A294125 A294126 A294127

Keyword

nonn,more,hard

Author

Robert Price, Oct 23 2017

Extensions

a(21) from Robert Price, Nov 17 2018

Status

approved