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

1,1

Comments

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

For n large a(n) is usually zero.

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A338106 A232462 A266141 * A326046 A231169 A297847

Adjacent sequences: A266144 A266145 A266146 * A266148 A266149 A266150

Keyword

base,nonn

Author

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

Status

approved