A282667 Numbers k such that (7*10^k + 107)/3 is prime.

1, 2, 4, 8, 12, 15, 21, 31, 48, 151, 723, 879, 1811, 3444, 5104, 5512, 5695, 6723, 9082, 14944, 15184, 18512, 35141, 81985, 123563, 155203, 165134, 165239

Offset

1,2

Comments

For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 3 followed by the digits 69 is prime (see Example section).

a(29) > 2*10^5.

Links

Table of n, a(n) for n=1..28.

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

Makoto Kamada, Search for 23w69.

Example

4 is in this sequence because (7*10^4 + 107)/3 = 23369 is prime.
Initial terms and associated primes:
a(1) = 1, 59;
a(2) = 2, 269;
a(3) = 4, 23369;
a(4) = 8, 233333369;
a(5) = 12, 2333333333369; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(7*10^# + 107)/3] &]

Crossrefs

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

Sequence in context: A354919 A288514 A350616 * A124395 A334167 A024908

Adjacent sequences: A282664 A282665 A282666 * A282668 A282669 A282670

Keyword

nonn,more,hard

Author

Robert Price, Feb 20 2017

Extensions

a(25)-a(28) from Robert Price, Feb 21 2018

Status

approved