A281144 Numbers k such that (302*10^k + 13)/9 is prime.

1, 4, 7, 9, 16, 33, 55, 63, 75, 195, 412, 766, 1083, 1657, 2254, 4972, 10053, 10605, 13413, 18085, 24595, 25161, 36441, 80638, 178369

Offset

1,2

Comments

For k > 0, numbers k such that the digits 33 followed by k-1 occurrences of the digit 5 followed by the digit 7 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 335w7.

Example

4 is in this sequence because (302*10^4 + 13)/9 = 335557 is prime.
Initial terms and associated primes:
a(1) = 1, 337;
a(2) = 4, 335557;
a(3) = 7, 335555557;
a(4) = 9, 33555555557;
a(5) = 16, 335555555555555557; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(302*10^# + 13)/9] &]

Crossrefs

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

Sequence in context: A010424 A044903 A359016 * A103073 A166742 A346554

Adjacent sequences: A281141 A281142 A281143 * A281145 A281146 A281147

Keyword

nonn,more,hard

Author

Robert Price, Jan 15 2017

Extensions

a(25) from Robert Price, Feb 08 2020

Status

approved