A291609 Numbers k such that (49*10^k - 67)/9 is prime.

1, 3, 4, 7, 10, 24, 37, 46, 63, 64, 91, 114, 367, 453, 1156, 1347, 1524, 7153, 10893, 13548, 15153, 43093, 61167, 184993

Offset: 1

Author

Robert Price, Aug 27 2017

Keywords

• nonn
• more
• hard

Comments

For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 4 followed by the digits 37 is prime (see Example section).

a(25) > 2*10^5.

Examples

			4 is in this sequence because (49*10^4 - 67)/9 = 54437 is prime.
Initial terms and associated primes:
a(1) = 1, 47;
a(2) = 3, 5437;
a(3) = 4, 54437;
a(4) = 7, 54444437;
a(5) = 10, 54444444437; etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 54w37.

Crossrefs

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

Programs

Mathematica

Select[Range[1, 100000], PrimeQ[(49*10^# - 67)/9] &]

Extensions

a(24) from Robert Price, Mar 15 2019