A293000 Numbers k such that (2*10^k - 23)/3 is prime.

2, 3, 4, 26, 44, 58, 73, 88, 211, 244, 1393, 2282, 4108, 6777, 7480, 14369, 16153, 21081, 24308, 27368, 43455, 51597, 55559, 67405, 88112, 148460, 288371, 297488

Offset

1,1

Comments

For k>1, numbers k-2 occurrences of the digit 6 followed by the digits 59 is prime (see Example section).

a(29) > 3*10^5.

Links

Table of n, a(n) for n=1..28.

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

Makoto Kamada, Search for 6w59

Example

4 is in this sequence because (2*10^4 - 23)/3 = 6659 is prime.
Initial terms and associated primes:
a(1) = 2, 59;
a(2) = 3, 659;
a(3) = 4, 6659;
a(4) = 26, 66666666666666666666666659;
a(5) = 44, 66666666666666666666666666666666666666666659; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[(2*10^# - 23)/3] &]

Crossrefs

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

Sequence in context: A171558 A044906 A255312 * A141565 A098549 A274677

Adjacent sequences: A292997 A292998 A292999 * A293001 A293002 A293003

Keyword

nonn,more,hard

Author

Robert Price, Sep 27 2017

Extensions

a(26) from Robert Price, Apr 24 2018

a(27)-a(28) from Robert Price, Jun 01 2023

Status

approved