A291924 Numbers k such that (17*10^k - 29)/3 is prime.

1, 2, 3, 9, 10, 12, 15, 44, 64, 464, 646, 879, 938, 1006, 1644, 2172, 2290, 2348, 2880, 4291, 17686, 31167, 57543

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 57 is prime (see Example section).

a(25) > 3*10^5.

Links

Table of n, a(n) for n=1..23.

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

Makoto Kamada, Search for 56w57.

Example

3 is in this sequence because (17*10^3 - 29)/3 = 5657 is prime.
Initial terms and associated primes:
a(1) = 1, 47;
a(2) = 2, 557;
a(3) = 3, 5657;
a(4) = 9, 5666666657;
a(5) = 10, 56666666657; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[(17*10^# - 29)/3] &]

Crossrefs

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

Sequence in context: A291610 A285428 A039012 * A357353 A214433 A257026

Adjacent sequences: A291921 A291922 A291923 * A291925 A291926 A291927

Keyword

nonn,more,hard

Author

Robert Price, Sep 05 2017

Status

approved