A266141 Number of n-digit primes in which n-1 of the digits are 2's.

4, 2, 3, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 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 2's and only the trailing digit can vary.

For n large a(n) is usually zero.

a(n) <= 4. If n > 1 and not a multiple of 3, then a(n) <= 2. It appears that a(n) <= 1 for n > 3. - Chai Wah Wu, Dec 26 2015

Examples

			a(3) = 3 since 223, 227 and 229 are all primes.
		

Links

• Dana Jacobsen, Table of n, a(n) for n = 1..10000 (first 1500 terms from Michael De Vlieger and Robert G. Wilson v)

Crossrefs

Cf. A265733, A266142, A266143, A266144, A266145, A266146, A266147, A266148, A266149, A084832, A096506, A099409, A099410.

Programs

Mathematica

d = 2; Array[Length@ Select[d (10^# - 1)/9 + (Range[0, 9] - d), PrimeQ] &, 100]

Perl

use ntheory ":all"; sub a266141 { my $n=shift; return 4 if $n==1; 0+scalar(grep{is_prime("2"x($n-1).$)} 1,3,7,9); } say a266141($) for 1..20; # Dana Jacobsen, Dec 27 2015

Python

from sympy import isprime
def A266141(n):
    return 4 if n==1 else sum(1 for d in '1379' if isprime(int('2'*(n-1)+d))) # Chai Wah Wu, Dec 26 2015