A289051 Numbers k such that 13*10^k + 1 is prime.

1, 2, 3, 7, 16, 53, 95, 105, 125, 163, 358, 423, 562, 1774, 3459, 13957, 17962, 51179, 65963, 72808

Offset

1,2

Comments

For k>0, numbers such that the digits 13 followed by k-1 occurrences of the digit 0 followed by the digit 1 is prime (see Example section).

a(21) > 10^5.

Links

Table of n, a(n) for n=1..20.

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

Makoto Kamada, Search for 130w1.

Example

2 is in this sequence because 13*10^3 + 1 = 1301 is prime.
Initial terms and primes associated:
a(1) = 1, 131;
a(2) = 2, 1301;
a(3) = 3, 13001;
a(4) = 7, 130000001;
a(5) = 16, 130000000000000001; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[13*10^# + 1] &]

Crossrefs

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

Sequence in context: A246829 A296231 A089125 * A282320 A002854 A036356

Adjacent sequences: A289048 A289049 A289050 * A289052 A289053 A289054

Keyword

nonn,more,hard

Author

Robert Price, Jun 22 2017

Status

approved