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

1,1

Comments

The leading digits must be 6'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 61 and 67 are prime.
a(3) = 1 since 661 is the only prime.

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 *)

Prog

(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

Crossrefs

Cf. A265733, A266141, A266142, A266143, A266144, A266146, A266147, A266148, A266149, A098088, A096507.

Sequence in context: A371077 A113092 A033324 * A365939 A266144 A016508

Adjacent sequences: A266142 A266143 A266144 * A266146 A266147 A266148

Keyword

base,nonn

Author

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

Status

approved