A278960 Numbers k such that 4*10^k - 99 is prime.

4, 6, 7, 9, 43, 53, 67, 69, 123, 178, 201, 448, 649, 658, 1068, 2003, 2584, 4445, 4816, 6322, 8477, 8868, 14500, 24934, 33412, 42504, 87287, 87337

Offset

1,1

Comments

For k>1, numbers such that the digit 3 followed by k-2 occurrences of the digit 9 followed by the digits 01 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 39w01.

Example

4 is in this sequence because 4*10^4 - 99 = 39901 is prime.
Initial terms and primes associated:
a(1) = 4, 39901;
a(2) = 6, 3999901;
a(3) = 7, 39999901;
a(4) = 9, 3999999901;
a(5) = 43, 39999999999999999999999999999999999999999901; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[4*10^# - 99] &]

Prog

(Magma) [n: n in [2..500] | IsPrime(4*10^n - 99)]; // Vincenzo Librandi, Dec 03 2016
(PARI) is(n)=ispseudoprime(4*10^n - 99) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

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

Sequence in context: A010418 A243193 A087790 * A344570 A340833 A340847

Adjacent sequences: A278957 A278958 A278959 * A278961 A278962 A278963

Keyword

nonn,more,hard

Author

Robert Price, Dec 02 2016

Extensions

Link and Mathematica program corrected by Robert Price, Jun 11 2018

Status

approved