A280449 Numbers k such that (2*10^k - 71)/3 is prime.

2, 3, 5, 6, 8, 11, 15, 25, 38, 54, 101, 105, 158, 295, 303, 389, 482, 558, 693, 1965, 3503, 9818, 13255, 30351, 51285, 54767, 57384, 88808, 109645, 174301, 187062

Offset

1,1

Comments

For k > 1, numbers k such that the number consisting of k-2 occurrences of the digit 6 followed by the digits 43 is prime (see Example section).

a(32) > 2*10^5.

Links

Table of n, a(n) for n=1..31.

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

Makoto Kamada, Search for 6w43.

Example

5 is in this sequence because (2*10^5 - 71) / 3 = 66643 is prime.
Initial terms and associated primes:
a(1) = 2, 43;
a(2) = 3, 643;
a(3) = 5, 66643;
a(4) = 6, 666643;
a(5) = 8, 66666643; etc.

Mathematica

Select[Range[2, 100000], PrimeQ[(2*10^# - 71) / 3] &]

Prog

(PARI) is(n)=isprime((2*10^n - 71)/3) \\ Charles R Greathouse IV, Jan 03 2017

Crossrefs

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

Sequence in context: A117517 A339732 A098491 * A107947 A120768 A271109

Adjacent sequences: A280446 A280447 A280448 * A280450 A280451 A280452

Keyword

nonn,more,hard

Author

Robert Price, Jan 03 2017

Extensions

a(29) - a(31) from Robert Price, Dec 31 2017

Status

approved