A266145 Number of n-digit primes in which n-1 of the digits are 6's.

4, 2, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 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, 1, 0, 0, 2, 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, 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 6's and only the trailing digit can vary.

For n large a(n) is usually zero.

Examples

			a(2) = 2 since 61 and 67 are prime.
a(3) = 1 since 661 is the only prime.
		

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, A266146, A266147, A266148, A266149, A098088, A096507.

Programs

Mathematica

d = 6; Array[Length@ Select[d (10^# - 1)/9 + (Range[0, 9] - d), PrimeQ] &, 100]
Join[{4},Table[Count[Table[10FromDigits[PadRight[{},k,6]]+n,{n,{1,3,7,9}}], ?PrimeQ],{k,110}]] (* _Harvey P. Dale, Dec 23 2017 *)

Python

from _future_ import division
from sympy import isprime
def A266145(n):
    return 4 if n==1 else sum(1 for d in [-5,-3,1,3] if isprime(2*(10**n-1)//3+d)) # Chai Wah Wu, Dec 27 2015