A283186 Numbers k such that 89*10^k - 7 is prime.

1, 2, 3, 19, 33, 42, 73, 259, 271, 297, 303, 324, 392, 623, 1218, 2801, 4273, 6071, 6383, 8699, 8706, 15139, 17163, 40491, 54518, 83976, 89687, 105284, 168614

Offset

1,2

Comments

For k>0, numbers such that the digits 88 followed by k-1 occurrences of the digit 9 followed by the digit 3 is prime (see Example section).

a(30) > 2*10^5.

Links

Table of n, a(n) for n=1..29.

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

Makoto Kamada, Search for 889w3.

Example

3 is in this sequence because 89*10^3 - 7 = 88993 is prime.
Initial terms and primes associated:
a(1) = 1, 883;
a(2) = 2, 8893;
a(3) = 3, 88993;
a(4) = 19, 889999999999999999993;
a(5) = 33, 88999999999999999999999999999999993; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[89*10^# - 7] &]

Crossrefs

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

Sequence in context: A142955 A213896 A088790 * A363498 A215304 A215281

Adjacent sequences: A283183 A283184 A283185 * A283187 A283188 A283189

Keyword

nonn,more,hard

Author

Robert Price, Mar 02 2017

Extensions

a(28)-a(29) from Robert Price, Apr 23 2020

Status

approved