A293035 Numbers k such that (22*10^k - 73)/3 is prime.

2, 3, 4, 17, 34, 35, 47, 65, 215, 254, 443, 676, 878, 1067, 1401, 1660, 1880, 8987, 14318, 14410, 52217, 54958, 63034, 171929

Offset

1,1

Comments

For k > 1, numbers k such that the digit 7 followed by k-2 occurrences of the digit 3 followed by the digits 09 is prime (see Example section).

a(25) > 2*10^5.

Links

Table of n, a(n) for n=1..24.

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

Makoto Kamada, Search for 73w09.

Example

3 is in this sequence because (22*10^3 - 73)/3 = 7309 is prime.
Initial terms and associated primes:
a(1) = 2, 709;
a(2) = 3, 7309;
a(3) = 4, 73309;
a(4) = 17, 733333333333333309;
a(5) = 34, 73333333333333333333333333333333309; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[(22*10^# - 73)/3] &]

Crossrefs

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

Sequence in context: A115891 A378417 A359230 * A037394 A037430 A377958

Adjacent sequences: A293032 A293033 A293034 * A293036 A293037 A293038

Keyword

nonn,more,hard

Author

Robert Price, Sep 28 2017

Extensions

a(24) from Robert Price, Apr 20 2019

Status

approved