OFFSET
1,3
COMMENTS
For k > 0, numbers k such that the digits 99 followed by k-1 occurrences of the digit 3 followed by the digit 1 is prime (see Example section).
a(29) > 3*10^5.
LINKS
Makoto Kamada, Factorization of near-repdigit-related numbers.
Makoto Kamada, Search for 993w1.
EXAMPLE
2 is in this sequence because (298*10^2 - 7)/3 = 9931 is prime.
Initial terms and associated primes:
a(1) = 0, 97;
a(2) = 1, 991;
a(3) = 2, 9931;
a(4) = 9, 99333333331;
a(5) = 16, 993333333333333331; etc.
MATHEMATICA
Select[Range[0, 100000], PrimeQ[(298*10^# - 7)/3] &]
CROSSREFS
KEYWORD
nonn,more,hard
AUTHOR
Robert Price, Jun 09 2017
EXTENSIONS
a(27) from Robert Price, Jun 09 2020
a(28) from Robert Price, Jun 21 2023
STATUS
approved