A281990 Numbers k such that (199*10^k - 7)/3 is prime.

1, 4, 16, 25, 27, 39, 109, 117, 720, 989, 1451, 1477, 1522, 2242, 2657, 2694, 2929, 5927, 7589, 7844, 9990, 19475, 43896, 44304, 95134, 128343, 129487

Offset

1,2

Comments

For k > 1, numbers k such that the digits 66 followed by k-1 occurrences of the digit 3 followed by the digit 1 is prime (see Example section).

a(28) > 3*10^5.

Links

Table of n, a(n) for n=1..27.

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

Makoto Kamada, Search for 663w1.

Example

4 is in this sequence because (199*10^4 - 7)/3 = 663331 is prime.
Initial terms and associated primes:
a(1) = 1, 661;
a(2) = 4, 663331;
a(3) = 16, 663333333333333331;
a(4) = 25, 663333333333333333333333331;
a(5) = 27, 66333333333333333333333333331; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(199*10^# - 7)/3] &]

Prog

(PARI) isok(k) = isprime((199*10^k - 7)/3); \\ Michel Marcus, Feb 04 2017

Crossrefs

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

Sequence in context: A173926 A305884 A239522 * A103052 A228004 A269157

Adjacent sequences: A281987 A281988 A281989 * A281991 A281992 A281993

Keyword

nonn,more,hard

Author

Robert Price, Feb 04 2017

Extensions

a(26)-a(27) from Robert Price, May 21 2020

Status

approved