A290433 Numbers k such that (85*10^k - 103)/9 is prime.

1, 3, 4, 16, 28, 45, 46, 67, 93, 130, 265, 321, 376, 717, 934, 1047, 1420, 2547, 5683, 8593, 9445, 31086, 33382, 43089, 76021, 90745

Offset

1,2

Comments

For k > 1, numbers k such that the digit 9 followed by k-2 occurrences of the digit 4 followed by the digits 33 is prime (see Example section).

a(27) > 2*10^5.

Links

Table of n, a(n) for n=1..26.

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

Makoto Kamada, Search for 94w33.

Example

3 is in this sequence because (85*10^3 - 103)/9 = 9433 is prime.
Initial terms and associated primes:
a(1) = 1, 83;
a(2) = 3, 9433;
a(3) = 4, 94433;
a(4) = 16, 94444444444444433;
a(5) = 28, 94444444444444444444444444433; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[85*10^# - 103)/9] &]

Crossrefs

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

Sequence in context: A108653 A316194 A123773 * A251582 A328773 A330693

Adjacent sequences: A290430 A290431 A290432 * A290434 A290435 A290436

Keyword

nonn,more,hard

Author

Robert Price, Oct 06 2017

Status

approved