A285785 Numbers k such that (22*10^k - 37)/3 is prime.

1, 3, 5, 6, 11, 12, 15, 21, 23, 25, 30, 64, 71, 72, 409, 1491, 1555, 4469, 5289, 7002, 16174, 16485, 68133, 73853, 134111

Offset

1,2

Comments

For k > 1, numbers k such that the digit 7 followed by k-2 occurrences of the digit 3 followed by the digits 21 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 73w21.

Example

3 is in this sequence because (22*10^3 - 37)/3 = 7321 is prime.
Initial terms and associated primes:
a(1) = 1, 61;
a(2) = 3, 7321;
a(3) = 5, 733321;
a(4) = 6, 7333321;
a(5) = 11, 733333333321; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[(22*10^# - 37)/3] &]

Crossrefs

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

Sequence in context: A358866 A167522 A001838 * A080759 A145714 A326310

Adjacent sequences: A285782 A285783 A285784 * A285786 A285787 A285788

Keyword

nonn,more,hard

Author

Robert Price, May 09 2017

Extensions

a(25) from Robert Price, Apr 15 2019

Status

approved