A291867 Numbers k such that (17*10^k - 41)/3 is prime.

1, 3, 5, 7, 13, 18, 45, 73, 165, 174, 298, 502, 563, 901, 1033, 1164, 1181, 2040, 4165, 20389, 23608, 34542, 88761

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 53 is prime (see Example section).

a(24) > 2*10^5.

Links

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

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

Makoto Kamada, Search for 56w53.

Example

3 is in this sequence because (17*10^3 - 41)/3 = 5653 is prime.
Initial terms and associated primes:
a(1) = 1, 43;
a(2) = 3, 5653;
a(3) = 5, 566653;
a(4) = 7, 56666653;
a(5) = 13, 56666666666653; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[(17*10^# - 41)/3] &]

Crossrefs

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

Sequence in context: A192294 A227531 A079481 * A219674 A075571 A077133

Adjacent sequences: A291864 A291865 A291866 * A291868 A291869 A291870

Keyword

nonn,more,hard

Author

Robert Price, Sep 04 2017

Status

approved