OFFSET
1,2
COMMENTS
For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 5 followed by the digits 13 is prime (see Example section).
a(22) > 2*10^5.
LINKS
Makoto Kamada, Factorization of near-repdigit-related numbers.
Makoto Kamada, Search for 45w13.
EXAMPLE
3 is in this sequence because (41*10^3 - 383)/9 = 4513 is prime.
Initial terms and associated primes:
a(1) = 1, 3;
a(2) = 3, 4513;
a(3) = 5, 455513;
a(4) = 6, 4555513;
a(5) = 21, 4555555555555555555513; etc.
MATHEMATICA
Select[Range[1, 100000], PrimeQ[(41*10^# - 383)/9] &]
PROG
(PARI) isok(k) = isprime((41*10^k - 383)/9); \\ Michel Marcus, Nov 22 2017
CROSSREFS
KEYWORD
nonn,more,hard
AUTHOR
Robert Price, Nov 21 2017
EXTENSIONS
a(20)-a(21) from Robert Price, Nov 16 2018
STATUS
approved