A272059 Numbers k such that (17*10^k + 13)/3 is prime.

1, 2, 4, 7, 10, 13, 15, 20, 22, 33, 34, 108, 117, 130, 193, 273, 280, 654, 775, 1144, 4014, 4015, 7701, 10356, 11478, 12427, 15075, 44107, 102597, 118635

Offset

1,2

Comments

For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 6 followed by the digits 71 is prime (see Example section).

a(31) > 2*10^5.

Links

Table of n, a(n) for n=1..30.

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

Makoto Kamada, Search for 56w71.

Example

4 is in this sequence because (17*10^4 + 13)/3 = 56671 is prime.
Initial terms and associated primes:
a(1) = 1, 61;
a(2) = 2, 571:
a(3) = 4, 56671;
a(4) = 7, 56666671;
a(5) = 10, 56666666671, etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(17*10^# + 13)/3] &]

Prog

(PARI) is(n)=ispseudoprime((17*10^n + 13)/3) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

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

Sequence in context: A122019 A190279 A186325 * A033627 A066512 A304116

Adjacent sequences: A272056 A272057 A272058 * A272060 A272061 A272062

Keyword

nonn,more

Author

Robert Price, May 19 2016

Extensions

a(29)-a(30) from Robert Price, Jan 22 2019

Status

approved