A290150 Numbers k such that (316*10^k - 1)/9 is prime.

2, 3, 8, 9, 11, 14, 17, 23, 29, 38, 50, 129, 164, 578, 1592, 2951, 4505, 16826, 17438, 22748

Offset

1,1

Comments

Numbers k such that the digits 35 followed by k occurrences of the digit 1 is prime (see Example section).

a(21) > 2*10^5.

Links

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

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

Makoto Kamada, Search for 351w.

Example

3 is in this sequence because (316*10^3 - 1)/9 = 35111 is prime.
Initial terms and associated primes:
a(1) = 2, 3511;
a(2) = 3, 35111;
a(3) = 8, 3511111111;
a(4) = 9, 35111111111;
a(5) = 11, 3511111111111; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(316*10^# - 1)/9] &]

Crossrefs

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

Sequence in context: A028821 A337261 A288740 * A237037 A283618 A284370

Adjacent sequences: A290147 A290148 A290149 * A290151 A290152 A290153

Keyword

nonn,more,hard

Author

Robert Price, Jul 21 2017

Status

approved