A283112 Numbers k such that (31*10^k - 1)/3 is prime.

1, 2, 3, 4, 6, 7, 8, 12, 18, 30, 75, 140, 212, 1639, 2167, 4663, 5526, 8582, 17636, 19922, 22470, 90064, 161582, 288238

Offset

1,2

Comments

For k>1, numbers such that the digits 10 followed by k occurrences of the digit 3 is prime (see Example section).

a(25) > 3*10^5.

Links

Table of n, a(n) for n=1..24.

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

Makoto Kamada, Search for 103w.

Example

3 is in this sequence because (31*10^3 - 1)/3 = 10333 is prime.
Initial terms and primes associated:
a(1) = 1, 103;
a(2) = 2, 1033;
a(3) = 3, 10333;
a(4) = 4, 103333;
a(5) = 6, 10333333; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(31*10^# - 1)/3] &]

Crossrefs

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

Sequence in context: A215068 A239011 A070525 * A174099 A099005 A336739

Adjacent sequences: A283109 A283110 A283111 * A283113 A283114 A283115

Keyword

nonn,more,hard

Author

Robert Price, Feb 28 2017

Extensions

a(23) from Robert Price, Feb 20 2020

a(24) from Robert Price, Jul 12 2023

Status

approved