A294631 Numbers k such that (59*10^k - 77)/9 is prime.

2, 3, 5, 6, 9, 14, 21, 29, 30, 32, 39, 59, 69, 113, 410, 13484, 15525, 16796, 22064, 37694, 38103, 73217

Offset

1,1

Comments

For k > 1, numbers k such that the digit 6 followed by k-2 occurrences of the digit 5 followed by the digits 47 is prime (see Example section).

a(23) > 2*10^5.

All terms == 0 or 2 (mod 3). - Robert Israel, May 30 2019

Links

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

Makoto Kamada, Factorization of near-repdigit-related numbers

Makoto Kamada, Search for 65w47.

Example

2 is in this sequence because (59*10^2 - 77)/9 = 647 is prime.
Initial terms and associated primes:
a(1) = 2, 647;
a(2) = 3, 6547;
a(3) = 5, 655547;
a(4) = 6, 6555547;
a(5) = 9, 6555555547; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[(59*10^# - 77)/9] &]

Prog

(PARI) is(n) = ispseudoprime((59*10^n - 77)/9) \\ Felix Fröhlich, May 30 2019

Crossrefs

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

Sequence in context: A181902 A295631 A278707 * A059454 A138538 A240555

Adjacent sequences: A294628 A294629 A294630 * A294632 A294633 A294634

Keyword

nonn,more,hard

Author

Robert Price, Nov 05 2017

Status

approved