A285377 Numbers k such that (41*10^k + 373)/9 is prime.

3, 5, 6, 9, 11, 53, 105, 125, 137, 228, 789, 1259, 1661, 1697, 1785, 3737, 6054, 7614, 11819, 27366, 28320, 48678, 69321, 76067, 97085

Offset: 1

Author

Robert Price, Apr 17 2017

Keywords

• nonn
• more
• hard

Comments

For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 5 followed by the digits 97 is prime (see Example section).

a(26) > 2*10^5.

Examples

			5 is in this sequence because (41*10^5 + 373)/9 = 455597 is prime.
Initial terms and associated primes:
a(1) = 3, 4597;
a(2) = 5, 455597;
a(3) = 6, 4555597;
a(4) = 9, 4555555597;
a(5) = 11, 455555555597; etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 45w97.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[(41*10^# + 373)/9] &]