A309742 Numbers k such that 8*10^(2*k) + 8*10^k + 1 are prime.

0, 1, 6, 11, 23, 297, 474, 1121, 2531, 3573, 5437, 5919

Offset: 1

Author

Seiichi Manyama, Aug 15 2019

Keywords

• nonn
• more

Examples

			           17 is prime. ==> a(1) = 0.
          881 is prime. ==> a(2) = 1.
        80801 = 7^2 * 17 * 97.
      8008001 = 47 * 170383.
    800080001 = 7 * 23 * 103 * 48247.
  80000800001 = 71 * 1126771831.
8000008000001 is prime. ==> a(3) = 6.
		

Crossrefs

Cf. A309739.

Programs

PARI

for(k=0, 1e3, if(ispseudoprime(8*100^k+8*10^k+1), print1(k", ")))

Python

from sympy import isprime
def afind(limit, startk=0):
    for k in range(startk, limit+1):
        if isprime(8*100**k + 8*10**k + 1): print(k, end=", ")
afind(500) # Michael S. Branicky, Dec 12 2021

Extensions

a(11) from Michael S. Branicky, Dec 12 2021

a(12) from Michael S. Branicky, Apr 16 2023