A295325 Numbers k such that 15*10^k + 1 is prime.

1, 4, 7, 8, 18, 19, 73, 143, 192, 408, 533, 792, 3179, 7709, 9554, 35598, 41587, 52919, 56021, 61604, 78672, 81624

Offset: 1

Author

Robert Price, Nov 19 2017

Keywords

• nonn
• more
• hard

Comments

For k > 1, numbers k such that the digits 15 followed by k-1 occurrences of the digit 0 followed by the digit 1 is prime (see Example section).

a(23) > 10^5.

Examples

			4 is in this sequence because 15*10^4 + 1 = 150001 is prime.
Initial terms and associated primes:
a(1) = 1, 151;
a(2) = 4, 150001;
a(3) = 7, 150000001;
a(4) = 8, 1500000001;
a(5) = 18, 15000000000000000001; etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 150w1.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[15*10^# + 1] &]

PARI

isok(k) = isprime(15*10^k + 1); \\ Michel Marcus, Nov 20 2017