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

1,1

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

Links

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

Example

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

Mathematica

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

Prog

(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
(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

Crossrefs

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

Sequence in context: A199081 A338106 A232462 * A266147 A326046 A231169

Adjacent sequences: A266138 A266139 A266140 * A266142 A266143 A266144

Keyword

base,nonn

Author

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

Status

approved