A293827 Numbers k such that (41*10^k - 59)/9 is prime.

2, 3, 11, 14, 15, 20, 23, 24, 39, 104, 374, 428, 698, 1436, 1521, 1800, 1809, 3848, 4796, 46314, 49182, 82044, 96137, 141836

Offset

1,1

Comments

For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 5 followed by the digits 49 is prime (see Example section).

a(25) > 2*10^5.

Links

Table of n, a(n) for n=1..24.

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

Makoto Kamada, Search for 45w49.

Example

3 is in this sequence because (41*10^3 - 59)/9 = 4549 is prime.
Initial terms and associated primes:
a(1) = 2, 449;
a(2) = 3, 4549;
a(3) = 11, 455555555549;
a(4) = 14, 455555555555549;
a(5) = 15, 4555555555555549; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[(41*10^# - 59)/9] &]

Crossrefs

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

Sequence in context: A105226 A139021 A176038 * A145771 A042473 A042665

Adjacent sequences: A293824 A293825 A293826 * A293828 A293829 A293830

Keyword

nonn,more,hard

Author

Robert Price, Oct 16 2017

Extensions

a(24) from Robert Price, Oct 27 2018

Status

approved