A280431 Numbers k such that (2*10^k - 41)/3 is prime.

2, 3, 4, 5, 8, 9, 27, 32, 39, 44, 101, 140, 268, 386, 695, 741, 1155, 1564, 1611, 4076, 6083, 11672, 26685, 50603, 134720

Offset

1,1

Comments

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

a(26) > 2*10^5.

Links

Table of n, a(n) for n=1..25.

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

Makoto Kamada, Search for 6w53.

Example

4 is in this sequence because (2*10^4 - 41) / 3 = 6653 is prime.
Initial terms and associated primes:
a(1) = 2, 53;
a(2) = 3, 653;
a(3) = 4, 6653;
a(4) = 5, 66653;
a(5) = 8, 66666653; etc.

Mathematica

Select[Range[2, 100000], PrimeQ[(2*10^# - 41) / 3] &]

Prog

(PARI) is(n)=ispseudoprime((2*10^n-41)/3) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

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

Sequence in context: A152606 A057911 A085266 * A056804 A305399 A101547

Adjacent sequences: A280428 A280429 A280430 * A280432 A280433 A280434

Keyword

nonn,more,hard

Author

Robert Price, Jan 02 2017

Extensions

a(25) from Robert Price, Feb 14 2018

Status

approved