A293531 Numbers k such that (268*10^k - 1)/3 is prime.

0, 2, 6, 7, 12, 13, 17, 18, 26, 77, 151, 222, 403, 567, 1107, 7221, 7722, 8475, 9729, 17904, 21404, 30170, 62523

Offset

1,2

Comments

Numbers k such that the digits 89 followed by k occurrences of the digit 3 is prime (see Example section).

a(24) > 10^5.

Links

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

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

Makoto Kamada, Search for 893w.

Example

2 is in this sequence because (268*10^2 - 1)/3 = 8933 is prime.
Initial terms and associated primes:
a(1) = 0, 89;
a(2) = 2, 8933;
a(3) = 6, 89333333;
a(4) = 7, 893333333;
a(5) = 12, 89333333333333; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(268*10^# - 1)/3] &]

Prog

(PARI) isok(k) = isprime((268*10^k - 1)/3); \\ Altug Alkan, Oct 11 2017

Crossrefs

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

Sequence in context: A371410 A217575 A172154 * A072147 A190121 A105329

Adjacent sequences: A293528 A293529 A293530 * A293532 A293533 A293534

Keyword

nonn,more,hard

Author

Robert Price, Oct 11 2017

Status

approved