A290115 Numbers k such that (7*10^k + 197)/3 is prime.

1, 3, 4, 6, 7, 52, 53, 103, 131, 199, 294, 426, 780, 1144, 1876, 2001, 3507, 5737, 6657, 12558, 28303, 31608, 60643, 74741, 124648

Offset

1,2

Comments

For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 3 followed by the digits 99 is prime (see Example section).

a(26) > 2*10^5.

Links

Table of n, a(n) for n=1..25.

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

Makoto Kamada, Search for 23w99.

Example

4 is in this sequence because (7*10^4 + 197)/3 = 23399 is prime.
Initial terms and associated primes:
a(1) = 1, 89;
a(2) = 3, 2399;
a(3) = 4, 23399;
a(4) = 6, 2333399;
a(5) = 7, 23333399; etc.

Maple

select(k -> isprime((7*10^k+197)/3), [$1..10000]); # Robert Israel, Jul 20 2017

Mathematica

Select[Range[0, 100000], PrimeQ[(7*10^# + 197)/3] &]

Crossrefs

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

Sequence in context: A289811 A161001 A168170 * A225794 A206769 A141219

Adjacent sequences: A290112 A290113 A290114 * A290116 A290117 A290118

Keyword

nonn,more,hard

Author

Robert Price, Jul 19 2017

Extensions

a(25) from Robert Price, Jul 17 2018

Status

approved