A294378 Numbers k such that (197*10^k - 11)/3 is prime.

1, 2, 5, 11, 24, 49, 50, 59, 67, 71, 91, 605, 726, 899, 1214, 3307, 3409, 3961, 11426, 30096, 70241, 80089, 108446

Offset

1,2

Comments

For k > 0, numbers k such that the digits 65 followed by k-1 occurrences of the digit 6 followed by the digit 3 is prime (see Example section).

a(24) > 2*10^5.

Links

Table of n, a(n) for n=1..23.

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

Makoto Kamada, Search for 656w3.

Example

2 is in this sequence because (197*10^2 - 11)/3 = 6563 is prime.
Initial terms and associated primes:
a(1) = 1, 653;
a(2) = 2, 6563;
a(3) = 5, 6566663;
a(4) = 11, 6566666666663;
a(5) = 24, 65666666666666666666666663; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(197*10^# - 11)/3] &]

Crossrefs

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

Sequence in context: A059776 A091360 A300277 * A090764 A182557 A027934

Adjacent sequences: A294375 A294376 A294377 * A294379 A294380 A294381

Keyword

nonn,more,hard

Author

Robert Price, Oct 29 2017

Extensions

a(23) from Robert Price, Mar 22 2020

Status

approved