A286431 Numbers k such that (22*10^k + 53)/3 is prime.

2, 3, 4, 5, 8, 9, 16, 17, 18, 36, 54, 69, 183, 200, 240, 846, 1424, 2511, 4750, 13854, 15414, 103450, 128094, 132746

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 51 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 73w51.

Example

3 is in this sequence because (22*10^3 + 53)/3 = 7351 is prime.
Initial terms and associated primes:
a(1) = 2, 751;
a(2) = 3, 7351;
a(3) = 4, 73351;
a(4) = 5, 733351;
a(5) = 8, 733333351; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(22*10^# + 53)/3] &]

Crossrefs

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

Sequence in context: A264886 A369294 A287117 * A015931 A330400 A306044

Adjacent sequences: A286428 A286429 A286430 * A286432 A286433 A286434

Keyword

nonn,more,hard

Author

Robert Price, May 09 2017

Extensions

a(22)-a(24) from Robert Price, Jul 06 2019

Status

approved