A289753 Numbers k such that 2*10^k - 43 is prime.

2, 6, 8, 13, 24, 38, 42, 47, 324, 338, 3957, 4243, 4623, 4692, 4824, 5741, 7611, 8403, 10499, 21386, 56083, 132493, 135083, 136057, 138162, 193981

Offset

1,1

Comments

For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 9 followed by the digits 57 is prime (see Example section).

a(27) > 2*10^5.

Links

Table of n, a(n) for n=1..26.

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

Makoto Kamada, Search for 19w57.

Example

6 is in this sequence because 2*10^6 - 43 = 1999957 is prime.
Initial terms and associated primes:
a(1) = 2, 157;
a(2) = 6, 1999957;
a(3) = 8, 199999957;
a(4) = 13, 19999999999957;
a(5) = 24, 1999999999999999999999957; etc.

Mathematica

Select[Range[2, 100000], PrimeQ[2*10^# - 43] &]

Crossrefs

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

Sequence in context: A294862 A087327 A266627 * A002511 A074383 A107505

Adjacent sequences: A289750 A289751 A289752 * A289754 A289755 A289756

Keyword

nonn,more,hard

Author

Robert Price, Jul 11 2017

Extensions

a(22)-a(26) from Robert Price, Apr 11 2018

Status

approved