A295826 Numbers k such that (202*10^k - 13)/9 is prime.

1, 2, 4, 20, 22, 34, 35, 41, 185, 547, 644, 713, 1489, 1885, 3211, 3257, 3625, 6733, 47732, 165569, 172940, 195383

Offset

1,2

Comments

For k > 0, numbers k such that the digits 22 followed by k-1 occurrences of the digit 4 followed by the digit 3 is prime (see Example section).

a(23) > 2*10^5.

Links

Table of n, a(n) for n=1..22.

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

Makoto Kamada, Search for 224w3.

Example

2 is in this sequence because (202*10^2 - 13)/9 = 2243 is prime.
Initial terms and associated primes:
a(1) = 1, 223;
a(2) = 2, 2243;
a(3) = 4, 224443;
a(4) = 20, 2244444444444444444443;
a(5) = 22, 224444444444444444444443; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(202*10^# - 13)/9] &]

Crossrefs

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

Sequence in context: A178223 A033180 A215815 * A201502 A069535 A108866

Adjacent sequences: A295823 A295824 A295825 * A295827 A295828 A295829

Keyword

nonn,more,hard

Author

Robert Price, Nov 28 2017

Extensions

a(20)-a(22) from Robert Price, Jan 08 2020

Status

approved