A295403 Numbers k such that (41*10^k - 383)/9 is prime.

1, 3, 5, 6, 21, 39, 114, 239, 246, 348, 906, 1115, 2801, 2958, 2982, 4275, 6581, 8736, 27051, 115523, 124335

Offset

1,2

Comments

For k > 1, numbers 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

Table of n, a(n) for n=1..21.

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 primes associated:
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

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

Sequence in context: A050563 A282809 A168156 * A272440 A276704 A103022

Adjacent sequences: A295400 A295401 A295402 * A295404 A295405 A295406

Keyword

nonn,more,hard

Author

Robert Price, Nov 21 2017

Extensions

a(20)-a(21) from Robert Price, Nov 16 2018

Status

approved