A293281 Numbers k such that (28*10^k + 149)/3 is prime.

0, 2, 4, 6, 10, 20, 40, 42, 46, 60, 68, 128, 516, 816, 1062, 3204, 3682, 4964, 5722, 11442, 17856, 41058, 60180, 85500, 104972

Offset

1,2

Comments

For k > 1, numbers k such that the digit 9 followed by k-2 occurrences of the digit 3 followed by the digits 83 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 93w83.

Example

4 is in this sequence because (28*10^4 + 149)/3 = 93383 is prime.
Initial terms and associated primes:
a(1) = 0, 59;
a(2) = 2, 983;
a(3) = 4, 93383;
a(4) = 6, 9333383;
a(5) = 10, 93333333383; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(28*10^# + 149)/3] &]
Join[{0}, Flatten[Position[Table[100*FromDigits[PadRight[{9}, n, 3]]+83, {n, 86000}], _?PrimeQ]]+1] (* Harvey P. Dale, Nov 01 2017 *)

Crossrefs

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

Sequence in context: A282251 A176716 A256056 * A164143 A095007 A005194

Adjacent sequences: A293278 A293279 A293280 * A293282 A293283 A293284

Keyword

nonn,more,hard

Author

Robert Price, Oct 04 2017

Extensions

a(25) from Robert Price, Dec 08 2019

Status

approved