A295032 Numbers k such that 12*10^k - 7 is prime.

0, 1, 2, 4, 5, 8, 11, 21, 25, 105, 191, 305, 463, 704, 1320, 1404, 1580, 1675, 2215, 3475, 6323, 10560, 28817, 30356, 98198

Offset

1,3

Comments

For k > 1, numbers k such that the digits 11 followed by k-1 occurrences of the digit 9 followed by the digit 3 is prime (see Example section).

a(26) > 3*10^5.

Links

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

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

Makoto Kamada, Search for 119w3.

Example

2 is in this sequence because 12*10^2 - 7 = 1193 is prime.
Initial terms and associated primes:
a(1) = 0, 5;
a(2) = 1, 113;
a(3) = 2, 1193;
a(4) = 4, 119993;
a(5) = 5, 1199993; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[12*10^# - 7 ] &]

Prog

(PARI) isok(k) = isprime(12*10^k - 7); \\ Michel Marcus, Nov 13 2017

Crossrefs

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

Sequence in context: A182564 A288523 A240179 * A280017 A080136 A080033

Adjacent sequences: A295029 A295030 A295031 * A295033 A295034 A295035

Keyword

nonn,more,hard

Author

Robert Price, Nov 12 2017

Status

approved