A293685 Numbers k such that (25*10^k - 67)/3 is prime.

1, 2, 3, 4, 39, 63, 64, 82, 129, 441, 685, 947, 1042, 1063, 1840, 2311, 8200, 9641, 15982, 17643, 45389, 54443, 100343, 102076, 124076

Offset

1,2

Comments

For k > 1, numbers k such that the digit 8 followed by k-2 occurrences of the digit 3 followed by the digits 11 is prime (see Example section).

a(26) > 2*10^5.

Links

Table of n, a(n) for n=1..25.

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

Makoto Kamada, Search for 83w11.

Example

2 is in this sequence because (25*10^2 - 67)/3 = 811 is prime.
Initial terms and associated primes:
a(1) = 1, 61;
a(2) = 2, 811;
a(3) = 3, 8311;
a(4) = 4, 83311;
a(5) = 39, 8333333333333333333333333333333333333311; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[(25*10^# - 67)/3] &]

Crossrefs

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

Sequence in context: A247961 A294921 A332534 * A078394 A375477 A273469

Adjacent sequences: A293682 A293683 A293684 * A293686 A293687 A293688

Keyword

nonn,more,hard

Author

Robert Price, Nov 10 2017

Extensions

a(23)-a(25) from Robert Price, Jun 19 2019

Status

approved