A295327 Numbers k such that 3*10^k - 13 is prime.

1, 13, 16, 19, 23, 25, 29, 30, 34, 53, 61, 89, 111, 191, 376, 1918, 2889, 12304, 17939, 18053, 31740, 56575, 65899

Offset

1,2

Comments

For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 9 followed by the digits 87 is prime (see Example section).

a(24) > 2*10^5.

Links

Table of n, a(n) for n=1..23.

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

Makoto Kamada, Search for 29w87.

Example

1 is in this sequence because 3*10^1 - 13 = 17 is prime.
Initial terms and associated primes:
a(1) = 1, 17;
a(2) = 13, 29999999999987;
a(3) = 16, 29999999999999987;
a(4) = 19, 29999999999999999987;
a(5) = 23, 299999999999999999999987; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[3*10^# - 13] &]

Prog

(PARI) isok(k) = isprime(3*10^k - 13); \\ Michel Marcus, Nov 20 2017

Crossrefs

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

Sequence in context: A348787 A064805 A246451 * A179202 A159975 A350300

Adjacent sequences: A295324 A295325 A295326 * A295328 A295329 A295330

Keyword

nonn,more,hard

Author

Robert Price, Nov 19 2017

Status

approved