A278418 Numbers k such that (83*10^k - 29) / 9 is prime.

1, 2, 4, 10, 28, 31, 32, 38, 68, 134, 158, 254, 311, 337, 392, 874, 2747, 3502, 4735, 6142, 14140, 17095, 20066, 21104, 26743

Offset

1,2

Comments

For k > 1, numbers k such that the digit 9 followed by k-2 occurrences of the digit 2 followed by the digits 19 is prime (see Example section).

a(26) > 2*10^5.

Links

Table of n, a(n) for n=1..25.

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

Makoto Kamada, Search for 92w19.

Example

4 is in this sequence because (83*10^4 - 29) / 9 = 92219 is prime.
Initial terms and associated primes:
a(1) = 1, 89;
a(2) = 2, 919;
a(3) = 4, 92219;
a(4) = 10, 92222222219;
a(5) = 28, 92222222222222222222222222219; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(83*10^# - 29) / 9] &]

Prog

(PARI) isok(n) = isprime((83*10^n - 29)/9); \\ Michel Marcus, Nov 21 2016

Crossrefs

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

Sequence in context: A005975 A048193 A123411 * A321946 A244485 A128933

Adjacent sequences: A278415 A278416 A278417 * A278419 A278420 A278421

Keyword

nonn,more,hard

Author

Robert Price, Nov 21 2016

Status

approved