A289943 Numbers k such that (304*10^k - 43)/9 is prime.

0, 2, 3, 6, 8, 9, 12, 24, 39, 93, 99, 147, 254, 416, 510, 572, 582, 1488, 1734, 5856, 19196, 40112, 124329

Offset

1,2

Comments

For k>0, numbers such that the digits 33 followed by k-1 occurrences of the digit 7 followed by the digit 3 is prime (see Example section).

a(24) > 2*10^5.

Links

Table of n, a(n) for n=1..23.

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

Makoto Kamada, Search for 337w3.

Example

3 is in this sequence because (304*10^3 - 43)/9 = 33773 is prime.
Initial terms and primes associated:
a(1) = 0, 29;
a(2) = 2, 3373;
a(3) = 3, 33773;
a(4) = 6, 33777773;
a(5) = 8, 3377777773; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(304*10^# - 43)/9] &]

Prog

(PARI) isok(k) = isprime((304*10^k - 43)/9); \\ Michel Marcus, Jul 16 2017

Crossrefs

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

Sequence in context: A047244 A111215 A099381 * A089437 A146768 A364958

Adjacent sequences: A289940 A289941 A289942 * A289944 A289945 A289946

Keyword

nonn,more,hard

Author

Robert Price, Jul 15 2017

Extensions

a(23) from Robert Price, Feb 17 2020

Status

approved