A294727 Numbers k such that (5*10^k - 173)/3 is prime.

2, 3, 5, 7, 13, 79, 98, 273, 1173, 3008, 3118, 4352, 4748, 5648, 11167, 11750, 12555, 26613, 88303

Offset

1,1

Comments

For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 6 followed by the digits 09 is prime (see Example section).

a(20) > 2*10^5.

Links

Table of n, a(n) for n=1..19.

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

Makoto Kamada, Search for 16w09.

Example

2 is in this sequence because (5*10^2 - 173)/3 = 109 is prime.
Initial terms and associated primes:
a(1) = 2, 109;
a(2) = 3, 1609;
a(3) = 5, 166609;
a(4) = 7, 16666609;
a(5) = 13, 16666666666609; etc.

Mathematica

Select[Range[2, 100000], PrimeQ[(5*10^# - 173)/3] &]

Prog

(PARI) isok(k) = isprime((5*10^k - 173)/3); \\ Michel Marcus, Nov 12 2017

Crossrefs

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

Sequence in context: A249797 A346686 A309249 * A348352 A007311 A031345

Adjacent sequences: A294724 A294725 A294726 * A294728 A294729 A294730

Keyword

nonn,more,hard

Author

Robert Price, Nov 11 2017

Status

approved