A294921 Numbers k such that (5*10^k + 97)/3 is prime.

2, 3, 4, 38, 46, 76, 82, 166, 180, 236, 909, 1668, 1884, 2042, 4602, 9830, 21939, 23956

Offset

1,1

Comments

For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 6 followed by the digits 99 is prime (see Example section).

a(19) > 2*10^5.

Links

Table of n, a(n) for n=1..18.

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

Makoto Kamada, Search for 16w99.

Example

2 is in this sequence because (5*10^2 + 97)/3 = 199 is prime.
Initial terms and associated primes:
a(1) = 2, 199;
a(2) = 3, 1699;
a(3) = 4, 16699;
a(4) = 38, 166666666666666666666666666666666666699;
a(5) = 46, 16666666666666666666666666666666666666666666699; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(5*10^# + 97)/3] &]
Select[Range[24000], PrimeQ[100*FromDigits[PadRight[{1}, #, 6]]+99]&]+1 (* Harvey P. Dale, Dec 12 2017 *)

Prog

(PARI) isok(k) = isprime((5*10^k + 97)/3); \\ Michel Marcus, Nov 15 2017

Crossrefs

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

Sequence in context: A084314 A308045 A247961 * A332534 A293685 A078394

Adjacent sequences: A294918 A294919 A294920 * A294922 A294923 A294924

Keyword

nonn,more,hard

Author

Robert Price, Nov 15 2017

Status

approved