A295323 Numbers k such that 2*10^k - 51 is prime.

2, 3, 4, 8, 11, 13, 17, 28, 56, 105, 231, 339, 643, 922, 1219, 1880, 2209, 4238, 4987, 14770, 56194, 67043, 96867, 124751

Offset

1,1

Comments

For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 9 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 19w49.

Example

2 is in this sequence because 2*10^2 - 51 = 149 is prime.
Initial terms and associated primes:
a(1) = 2, 149;
a(2) = 3, 1949;
a(3) = 4, 19949;
a(4) = 8, 199999949;
a(5) = 11, 199999999949; etc.

Mathematica

Select[Range[2, 100000], PrimeQ[2*10^# - 51] &]

Prog

(PARI) isok(k) = isprime(2*10^k - 51); \\ Michel Marcus, Nov 20 2017

Crossrefs

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

Sequence in context: A275646 A279194 A050727 * A102951 A015935 A135909

Adjacent sequences: A295320 A295321 A295322 * A295324 A295325 A295326

Keyword

nonn,more,hard

Author

Robert Price, Nov 19 2017

Extensions

a(24) from Robert Price, Apr 13 2018

Status

approved