A285939 Numbers k such that (19*10^k - 61)/3 is prime.

1, 2, 4, 10, 17, 33, 51, 63, 92, 441, 517, 578, 1252, 1456, 2261, 4857, 8420, 9872, 13444, 14175, 16316, 28978, 30865, 84409, 145499

Offset

1,2

Comments

For k > 1, numbers k such that the digit 6 followed by k-2 occurrences of the digit 3 followed by the digits 13 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 63w13.

Example

4 is in this sequence because (19*10^4 - 61)/3 = 63313 is prime.
Initial terms and associated primes:
a(1) = 1, 43;
a(2) = 2, 613;
a(3) = 4, 63313;
a(4) = 10, 63333333313;
a(5) = 17, 633333333333333313; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[(19*10^# - 61)/3] &]

Crossrefs

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

Sequence in context: A244474 A301739 A152231 * A034455 A057491 A005541

Adjacent sequences: A285936 A285937 A285938 * A285940 A285941 A285942

Keyword

nonn,more,hard

Author

Robert Price, Apr 29 2017

Extensions

a(25) from Robert Price, May 04 2019

Status

approved