A293027 Numbers k such that (23*10^k - 83)/3 is prime.

2, 3, 5, 6, 16, 146, 234, 272, 291, 419, 435, 470, 501, 900, 3080, 3360, 7881, 10865, 13994, 20031, 38184, 43802, 89705, 165060, 168608

Offset

1,1

Comments

For k>1, numbers such that the digit 7 followed by k-2 occurrences of the digit 6 followed by the digits 39 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 76w39.

Example

3 is in this sequence because (23*10^3 - 83)/3 = 7639 is prime.
Initial terms and primes associated:
a(1) = 2, 739;
a(2) = 3, 7639;
a(3) = 5, 766639;
a(4) = 6, 7666639;
a(5) = 16, 76666666666666639; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[(23*10^# - 83)/3] &]

Crossrefs

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

Sequence in context: A079226 A055686 A126250 * A276353 A109628 A192367

Adjacent sequences: A293024 A293025 A293026 * A293028 A293029 A293030

Keyword

nonn,more,hard

Author

Robert Price, Sep 28 2017

Extensions

a(24)-a(25) from Robert Price, Aug 12 2019

Status

approved