A294379 Numbers k such that (62*10^k - 197)/9 is prime.

1, 5, 7, 14, 17, 40, 53, 95, 97, 113, 122, 125, 145, 374, 470, 485, 1685, 5324, 8035, 10745, 52448, 68059

Offset

1,2

Comments

For k > 1, numbers k such that the digit 6 followed by k-2 occurrences of the digit 8 followed by the digits 67 is prime (see Example section).

a(23) > 2*10^5.

Links

Table of n, a(n) for n=1..22.

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

Makoto Kamada, Search for 68w67.

Example

5 is in this sequence because (62*10^5 - 197)/9 = 6263 is prime.
Initial terms and associated primes:
a(1) = 1, 47;
a(2) = 5, 688867;
a(3) = 7, 68888867;
a(4) = 14, 688888888888867;
a(5) = 17, 688888888888888867; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[(62*10^# - 197)/9] &]

Crossrefs

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

Sequence in context: A301686 A314343 A105638 * A314344 A314345 A314346

Adjacent sequences: A294376 A294377 A294378 * A294380 A294381 A294382

Keyword

nonn,more,hard

Author

Robert Price, Oct 29 2017

Status

approved