A254441 Numbers k such that (41*10^k + 49)/9 is prime.

2, 3, 6, 20, 26, 38, 51, 119, 155, 218, 446, 486, 1211, 1319, 1338, 1365, 1575, 5106, 7019, 9503, 9695, 14304, 15417, 17765, 24222, 25500, 26306, 35238, 93207

Offset: 1

Author

Robert Price, Apr 17 2016

Keywords

• nonn
• more

Comments

For terms k > 1, numbers that begin with the digit 4 followed by k-2 occurrences of the digit 5 followed by the digits 61 are prime (see Example section).

a(30) > 2*10^5.

Examples

			3 is in this sequence because (41*10^3 + 49)/9 = 4561 is prime.
Initial terms and associated primes:
a(1) = 2, 461;
a(2) = 3, 4561;
a(3) = 6, 4555561;
a(4) = 20, 455555555555555555561;
a(5) = 26, 455555555555555555555555561, etc.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..29
• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 45w61.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[(41*10^# + 49)/9] &]

PARI

is(n)=ispseudoprime((41*10^n + 49)/9) \\ Charles R Greathouse IV, Jun 13 2017