A289752 Numbers k such that (4*10^k - 79)/3 is prime.

2, 3, 8, 11, 20, 24, 32, 33, 60, 86, 162, 410, 816, 1809, 1920, 2499, 2922, 7205, 8238, 15990, 37163, 115668, 141926, 179963

Offset

1,1

Comments

For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 3 followed by the digits 07 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 13w07.

Example

3 is in this sequence because (4*10^3 - 79)/3 = 1307 is prime.
Initial terms and associated primes:
a(1) = 2, 107;
a(2) = 3, 1307;
a(3) = 8, 133333307;
a(4) = 11, 133333333307;
a(5) = 20, 133333333333333333307; etc.

Mathematica

Select[Range[2, 100000], PrimeQ[(4*10^# - 79)/3] &]

Crossrefs

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

Sequence in context: A042263 A280323 A153439 * A119064 A285113 A335632

Adjacent sequences: A289749 A289750 A289751 * A289753 A289754 A289755

Keyword

nonn,more,hard

Author

Robert Price, Jul 11 2017

Extensions

a(22)-a(24) from Robert Price, Feb 14 2018

Status

approved