A293398 Numbers k such that (728*10^k - 71)/9 is prime.

0, 2, 5, 6, 11, 14, 41, 47, 51, 84, 164, 228, 293, 1178, 1212, 1292, 2099, 2694, 4446, 7382, 13638, 39428, 40971

Offset

1,2

Comments

For k > 0, numbers k such that the digits 80 followed by k-1 occurrences of the digit 8 followed by the digit 1 is prime (see Example section).

a(24) > 2*10^5.

Links

Table of n, a(n) for n=1..23.

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

Makoto Kamada, Search for 808w1.

Example

2 is in this sequence because (728*10^2 - 71)/9 = 8081 is prime.
Initial terms and associated primes:
a(1) = 0, 73;
a(2) = 2, 8081;
a(3) = 5, 8088881;
a(4) = 6, 80888881;
a(5) = 11, 8088888888881; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(728*10^# - 71)/9] &]

Prog

(PARI) isok(k) = isprime((728*10^k - 71)/9); \\ Altug Alkan, Oct 08 2017

Crossrefs

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

Sequence in context: A135013 A239447 A336527 * A180323 A103035 A088273

Adjacent sequences: A293395 A293396 A293397 * A293399 A293400 A293401

Keyword

nonn,more,hard

Author

Robert Price, Oct 08 2017

Status

approved