A266144 Number of n-digit primes in which n-1 of the digits are 5's.

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

Offset

1,1

Comments

The leading digits must be 5'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(2) = 2 since 53 and 59 are primes.
a(3) = 1 since 557 is the only prime.

Mathematica

d = 5; Array[Length@ Select[d (10^# - 1)/9 + (Range[0, 9] - d), PrimeQ] &, 100]

Prog

(Python)
from __future__ import division
from sympy import isprime
def A266144(n):
    return 4 if n==1 else sum(1 for d in [-4, -2, 2, 4] if isprime(5*(10**n-1)//9+d)) # Chai Wah Wu, Dec 27 2015

Crossrefs

Cf. A265733, A266141, A266142, A266143, A266145, A266146, A266147, A266148, A266149, A099415, A099416, A099417, A099418.

Sequence in context: A033324 A266145 A365939 * A016508 A351986 A325496

Adjacent sequences: A266141 A266142 A266143 * A266145 A266146 A266147

Keyword

base,nonn

Author

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

Status

approved