A278335 Numbers k such that 9*10^k + 89 is prime.

1, 4, 5, 7, 9, 15, 26, 43, 75, 106, 129, 141, 147, 171, 351, 512, 927, 1156, 2563, 2689, 3274, 4211, 5709, 6908, 11781, 14464, 31451, 34921, 36635, 38087, 55707, 59617, 104361, 123549

Offset

1,2

Comments

For k > 1, numbers k such that the digit 9 followed by k-2 occurrences of the digit 0 followed by the digits 89 is prime (see Example section).

a(35) > 2*10^5.

Links

Table of n, a(n) for n=1..34.

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

Makoto Kamada, Search for 90w89.

Example

4 is in this sequence because 9*10^4 + 89 = 90089 is prime.
Initial terms and associated primes:
a(1) = 1, 179;
a(2) = 4, 90089;
a(3) = 5, 900089;
a(4) = 7, 90000089;
a(5) = 9, 9000000089; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[9*10^# + 89] &]

Prog

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

Crossrefs

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

Sequence in context: A035266 A035264 A234257 * A243300 A231575 A335001

Adjacent sequences: A278332 A278333 A278334 * A278336 A278337 A278338

Keyword

nonn,more,hard

Author

Robert Price, Nov 18 2016

Extensions

a(33)-a(34) from Robert Price, Nov 09 2019

Status

approved