A276846 Numbers k such that (4*10^k + 143) / 3 is prime.

1, 2, 3, 4, 7, 9, 15, 21, 22, 44, 49, 53, 63, 127, 145, 393, 856, 1006, 1883, 2263, 5684, 13324, 14291, 27435, 38897, 114076

Offset: 1

Author

Robert Price, Sep 20 2016

Keywords

• nonn
• more

Comments

For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 3 followed by the digits 81 is prime (see Example section).

a(27) > 2*10^5.

Examples

			2 is in this sequence because (4*10^2 + 143) / 3 = 1381 is prime.
Initial terms and associated primes:
a(1) = 1, 61;
a(2) = 2, 181;
a(3) = 3, 1381;
a(4) = 4, 13381;
a(5) = 7, 13333381, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 13w81.

Crossrefs

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

Programs

Magma

[n: n in [0..500] | IsPrime((4*10^n+143) div 3)]; // Vincenzo Librandi, Sep 22 2016

Mathematica

Select[Range[0, 100000], PrimeQ[(4*10^# + 143) / 3] &]

PARI

is(n) = ispseudoprime((4*10^n + 143) / 3); \\ Altug Alkan, Sep 20 2016

Extensions

a(26) from Robert Price, Mar 05 2018