A275410 Numbers k such that (493*10^k - 7)/9 is prime.

1, 2, 5, 7, 8, 14, 19, 22, 23, 31, 62, 65, 79, 178, 356, 401, 517, 557, 1040, 2248, 6718, 10730, 15079, 24938, 36241, 58486, 69340

Offset: 1

Author

Robert Price, Jul 26 2016

Keywords

• nonn
• more

Comments

Numbers k such that the digits 54 followed by k occurrences of the digit 7 is prime (see Example section).

a(28) > 10^5.

Examples

			5 is in this sequence because (493*10^5-7)/9 = 5477777 is prime.
Initial terms and associated primes:
a(1) = 1, 547;
a(2) = 2, 5477;
a(3) = 5, 5477777;
a(4) = 7, 547777777;
a(5) = 8, 5477777777, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 547w.

Crossrefs

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

Programs

Magma

[n: n in [0..500] | IsPrime((493*10^n-7) div 9)]; // Vincenzo Librandi, Jul 27 2016

Mathematica

Select[Range[0, 100000], PrimeQ[(493*10^#-7)/9] &]

PARI

is(n)=ispseudoprime((493*10^n-7)/9) \\ Charles R Greathouse IV, Jun 13 2017