A266147 Number of n-digit primes in which n-1 of the digits are 8's.

4, 2, 3, 1, 1, 1, 0, 1, 2, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Michael De Vlieger and Robert G. Wilson v, Dec 21 2015

Keywords

• base
• nonn

Comments

The leading digits must be 8's and only the trailing digit can vary.

For n large a(n) is usually zero.

Examples

			a(3) = 3 since 881, 883, and 887 are all primes.
		

Links

• Michael De Vlieger and Robert G. Wilson v, Table of n, a(n) for n = 1..1500

Crossrefs

Cf. A265733, A266141, A266142, A266143, A266144, A266145, A266146, A266148, A266149, A099421, A099422, A096846, A096508.

Programs

Mathematica

d = 8; Array[Length@ Select[d (10^# - 1)/9 + (Range[0, 9] - d), PrimeQ] &, 100]
Join[{4},Table[Count[Table[10FromDigits[PadRight[{},k,8]]+n,{n,{1,3,7,9}}], ?PrimeQ],{k,110}]] (* _Harvey P. Dale, Jun 22 2021 *)

Python

from _future_ import division
from sympy import isprime
def A266147(n):
    return 4 if n==1 else sum(1 for d in [-7,-5,-1,1] if isprime(8*(10**n-1)//9+d)) # Chai Wah Wu, Dec 27 2015