A295398 Numbers k such that (305*10^k + 1)/9 is prime.

2, 3, 12, 14, 38, 126, 147, 152, 216, 285, 774, 1458, 2049, 3369, 5718, 8358, 12510, 13863, 30308, 38732, 128198

Offset

1,1

Comments

For k > 1, numbers k such that the digits 33 followed by k-1 occurrences of the digit 8 followed by the digit 9 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 338w9.

Example

2 is in this sequence because (305*10^2 + 1)/9 = 3389 is prime.
Initial terms and associated primes:
a(1) = 2, 3389;
a(2) = 3, 33889;
a(3) = 12, 33888888888889;
a(4) = 14, 3388888888888889;
a(5) = 38, 3388888888888888888888888888888888888889; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(305*10^# + 1)/9] &]

Prog

(PARI) isok(k) = isprime((305*10^k + 1)/9); \\ Michel Marcus, Nov 22 2017

Crossrefs

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

Sequence in context: A299545 A068603 A045878 * A138321 A015756 A163906

Adjacent sequences: A295395 A295396 A295397 * A295399 A295400 A295401

Keyword

nonn,more,hard

Author

Robert Price, Nov 21 2017

Extensions

a(21) from Robert Price, Jan 31 2020

Status

approved