A276311 Numbers k such that (13*10^k + 197)/3 is prime.

1, 2, 4, 5, 17, 21, 23, 28, 41, 43, 51, 59, 105, 115, 131, 273, 585, 1519, 2303, 4791, 4921, 6019, 7833, 25711, 27319, 32497, 37975, 49381, 87199

Offset

1,2

Comments

For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 3 followed by the digits 99 is prime (see the Example section).

a(30) > 10^5.

Links

Table of n, a(n) for n=1..29.

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

Makoto Kamada, Search for 43w99.

Example

4 is in this sequence because (13*10^4 + 197)/3 = 43399 is prime.
Initial terms and associated primes:
a(1) = 1, 109;
a(2) = 2, 499;
a(3) = 4, 43399;
a(4) = 5, 433399;
a(5) = 17, 433333333333333399, etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(13*10^# + 197)/3] &]

Prog

(PARI) is(n)=ispseudoprime((13*10^n+197)/3) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

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

Sequence in context: A169602 A092051 A065063 * A056440 A101843 A192117

Adjacent sequences: A276308 A276309 A276310 * A276312 A276313 A276314

Keyword

nonn,more,changed

Author

Robert Price, Aug 29 2016

Status

approved