A266148 Number of n-digit primes in which n-1 of the digits are 9's.

4, 6, 7, 7, 8, 10, 7, 13, 8, 8, 11, 13, 8, 11, 13, 14, 10, 9, 7, 11, 9, 13, 10, 19, 5, 10, 14, 7, 10, 9, 9, 15, 13, 8, 7, 9, 10, 11, 10, 13, 5, 12, 15, 7, 12, 7, 12, 11, 13, 11, 8, 13, 13, 13, 12, 12, 9, 9, 15, 14, 9, 8, 13, 11, 15, 17, 10, 8, 11, 10, 6, 16, 8, 8, 8, 15, 9, 11, 14, 7, 10, 11, 16, 17, 11, 10, 12, 16, 8, 15, 7, 11, 11, 10, 7, 12, 6, 10, 8, 9

Offset: 1

Author

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

Keywords

• base
• nonn

Comments

The other digit cannot be 0, 3, 6, or 9, or else the number would not be prime. - N. J. A. Sloane, May 20 2016

Examples

			a(3) = 7 since 199, 499, 599, 919, 929, 991 and 997 are all the three-digit primes containing two 9's.
		

Links

• Dana Jacobsen, Table of n, a(n) for n = 1..2500 (first 1215 terms from Michael De Vlieger and Robert G. Wilson v)

Crossrefs

Cf. A265733, A266141, A266142, A266143, A266144, A266145, A266146, A266147, A266149, A095714, A089675.

Programs

Mathematica

f9[n_] := Block[{cnt = k = 0, r = 9 (10^n - 1)/9, s = Range[0, 9] - 9}, While[k < n, cnt += Length@ Select[r + 10^k * s, PrimeQ@ # && IntegerLength@ # > k &]; k++]; cnt]; Array[f9, 100]

Perl

use ntheory ":all"; sub a266148 { my $n = shift; vecsum( map { my $k=$; scalar grep { is_prime("9" x $k . $ . "9" x ($n-$k-1)) } 0+($k>0) .. 8 } 0 .. $n-1 ); } # Dana Jacobsen, Jan 01 2016

Python

from sympy import isprime
def A266148(n):
    return sum(1 for d in range(-9,1) for i in range(n) if isprime(10**n-1+d*10**i)) # Chai Wah Wu, Dec 31 2015