A294123 Numbers k such that 4*10^k - 83 is prime.

2, 3, 6, 12, 24, 31, 33, 45, 66, 109, 150, 187, 345, 1000, 1026, 1189, 1959, 2754, 3405, 5047, 16291, 29958, 41547, 41709, 48908, 72274, 100257, 103981

Offset

1,1

Comments

For k > 1, numbers k such that the digit 3 followed by k-2 occurrences of the digit 9 followed by the digits 17 is prime (see Example section).

a(29) > 2*10^5.

Links

Table of n, a(n) for n=1..28.

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

Makoto Kamada, Search for 39w17.

Example

3 is in this sequence because 4*10^3 - 83 = 3917 is prime.
Initial terms and associated primes:
a(1) = 2, 317;
a(2) = 3, 3917;
a(3) = 6, 3999917;
a(4) = 12, 3999999999917;
a(5) = 24, 3999999999999999999999917; etc.

Mathematica

Select[Range[2, 100000], PrimeQ[4*10^# - 83] &]

Crossrefs

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

Sequence in context: A103341 A023675 A029996 * A321048 A038085 A124313

Adjacent sequences: A294120 A294121 A294122 * A294124 A294125 A294126

Keyword

nonn,more,hard

Author

Robert Price, Oct 23 2017

Extensions

a(27)-a(28) from Robert Price, Oct 04 2018

Status

approved