A281991 Numbers k such that (598*10^k - 31)/9 is prime.

1, 4, 5, 7, 16, 17, 19, 28, 59, 68, 128, 307, 343, 368, 421, 448, 469, 691, 1949, 2506, 4868, 6914, 30025, 30955, 35522, 43388, 45716, 49999, 76309, 80149

Offset

1,2

Comments

For k>=1, numbers such that the digits 66 followed by k-1 occurrences of the digit 4 followed by the digit 1 is prime (see Example section).

a(31) > 2*10^5.

Links

Table of n, a(n) for n=1..30.

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

Makoto Kamada, Search for 664w1.

Example

4 is in this sequence because (598*10^4 - 31)/9 = 664441 is prime.
Initial terms and primes associated:
a(1) = 1, 661;
a(2) = 4, 664441;
a(3) = 5, 6644441;
a(4) = 7, 664444441;
a(5) = 16, 664444444444444441; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(598*10^# - 31)/9] &]

Prog

(PARI) isok(k) = isprime((598*10^k - 31)/9); \\ Michel Marcus, Feb 04 2017

Crossrefs

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

Sequence in context: A072215 A106170 A353246 * A216537 A085195 A107289

Adjacent sequences: A281988 A281989 A281990 * A281992 A281993 A281994

Keyword

nonn,more,hard

Author

Robert Price, Feb 04 2017

Status

approved