A295626 Numbers k such that (424*10^k - 1)/9 is prime.

0, 3, 11, 33, 53, 78, 111, 144, 155, 191, 258, 687, 927, 1829, 5406, 11027, 14526, 19758, 20658, 37865, 61770, 87930

Offset

1,2

Comments

For k > 1, numbers k such that the digits 47 followed by k occurrences of the digit 1 is prime (see Example section).

a(23) > 2*10^5.

Links

Table of n, a(n) for n=1..22.

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

Makoto Kamada, Search for 471w.

Example

3 is in this sequence because (424*10^3 - 1)/9 = 47111 is prime.
Initial terms and associated primes:
a(1) = 0, 47;
a(2) = 3, 47111;
a(3) = 11, 4711111111111;
a(4) = 33, 47111111111111111111111111111111111; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(424*10^# - 11)/9] &]

Crossrefs

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

Sequence in context: A125671 A034561 A131747 * A079996 A288038 A186308

Adjacent sequences: A295623 A295624 A295625 * A295627 A295628 A295629

Keyword

nonn,more,hard

Author

Robert Price, Nov 24 2017

Status

approved