A282457 Numbers k such that 7*10^k - 47 is prime.

1, 2, 5, 8, 11, 14, 15, 30, 31, 42, 69, 85, 120, 128, 449, 685, 686, 741, 1291, 1521, 2165, 9110, 9150, 11366, 13154, 33321, 40758, 50789, 51440, 65492, 82509, 93887, 266024

Offset

1,2

Comments

For k > 1, numbers k such that the digit 6 followed by k-2 occurrences of the digit 9 followed by the digits 53 is prime (see Example section).

a(34) > 3*10^5.

Links

Table of n, a(n) for n=1..33.

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

Makoto Kamada, Search for 69w53.

Example

2 is in this sequence because 7*10^2 - 47 = 653 is prime.
Initial terms and associated primes:
a(1) = 1, 23;
a(2) = 2, 653;
a(3) = 5, 699953;
a(4) = 8, 699999953;
a(5) = 11, 699999999953; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[7*10^# - 47] &]

Crossrefs

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

Sequence in context: A294391 A257771 A276881 * A329848 A059560 A022842

Adjacent sequences: A282454 A282455 A282456 * A282458 A282459 A282460

Keyword

nonn,more,hard

Author

Robert Price, Feb 15 2017

Extensions

Reordered terms into ascending order by Robert Price, Apr 01 2022

a(33) from Robert Price, Oct 25 2023

Status

approved