A278426 Numbers k such that (26*10^k - 89) / 9 is prime.

1, 3, 4, 13, 15, 21, 27, 63, 70, 123, 136, 178, 208, 265, 411, 457, 856, 2401, 4642, 8017, 8211, 8385, 12337, 20793, 123970, 189928

Offset

1,2

Comments

For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 8 followed by the digits 79 is prime (see Example section).

a(27) > 2*10^5.

Links

Table of n, a(n) for n=1..26.

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

Makoto Kamada, Search for 28w79.

Example

4 is in this sequence because (26*10^4 - 89) / 9 = 28879 is prime.
Initial terms and associated primes:
a(1) = 1, 19;
a(2) = 3, 2879;
a(3) = 4, 28879;
a(4) = 13, 28888888888879;
a(5) = 15, 2888888888888879; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(26*10^# - 89) / 9] &]

Prog

(PARI) is(n)=ispseudoprime((26*10^n-89)/9) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

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

Sequence in context: A053910 A105074 A208847 * A293280 A087884 A057570

Adjacent sequences: A278423 A278424 A278425 * A278427 A278428 A278429

Keyword

nonn,more,hard

Author

Robert Price, Nov 21 2016

Extensions

a(25)-a(26) from Robert Price, Jun 16 2018

Status

approved