A275524 Numbers k such that (56*10^k + 223)/9 is prime.

0, 2, 3, 5, 8, 32, 36, 53, 92, 126, 156, 158, 536, 639, 846, 1356, 1953, 2237, 4407, 5082, 17447, 17922, 24806, 25926, 29699, 30474, 37424, 63942

Offset: 1

Author

Robert Price, Jul 31 2016

Keywords

• nonn
• more

Comments

For k > 1, numbers k such that the digit 6 followed by k-2 occurrences of the digit 2 followed by the digits 47 is prime (see Example section).

a(29) > 10^5.

Examples

			3 is in this sequence because (56*10^3 + 223)/9 = 6247 is prime.
Initial terms and associated primes:
a(1) = 0, 31;
a(2) = 2, 647;
a(3) = 3, 6247;
a(4) = 5, 622247;
a(5) = 8, 622222247, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 62w47.

Crossrefs

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

Programs

Magma

[n: n in [0..500] | IsPrime((56*10^n+223) div 9)]; // Vincenzo Librandi, Aug 01 2016

Mathematica

Select[Range[0, 100000], PrimeQ[(56*10^# + 223)/9] &]

PARI

is(n)=ispseudoprime((56*10^n+223)/9) \\ Charles R Greathouse IV, Jun 13 2017