A276545 Numbers k such that (43*10^k - 421)/9 is prime.

2, 5, 7, 8, 11, 13, 25, 26, 61, 82, 131, 289, 377, 547, 845, 929, 1786, 5887, 6562, 10546, 28033, 33493, 150515, 205183

Offset: 1

Author

Robert Price, Apr 09 2017

Keywords

• nonn
• more
• hard

Comments

For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 7 followed by the digits 31 is prime (see Example section).

a(25) > 3*10^5.

Examples

			4 is in this sequence because (43*10^4 - 421)/9 = 477731 is prime.
Initial terms and associated primes:
a(1) = 2, 431;
a(2) = 5, 477731;
a(3) = 7, 47777731;
a(4) = 8, 477777731;
a(5) = 11, 477777777731; etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 47w31.

Crossrefs

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

Programs

Mathematica

Select[Range[1, 100000], PrimeQ[(43*10^# - 421)/9] &]

Extensions

a(23) from Robert Price, Jan 21 2019

a(24) from Robert Price, Oct 25 2023