A266142 Number of n-digit primes in which n-1 of the digits are 3's.

4, 8, 9, 12, 7, 14, 13, 11, 8, 7, 9, 8, 3, 10, 11, 14, 9, 12, 6, 11, 11, 11, 9, 10, 9, 10, 22, 10, 10, 12, 7, 14, 14, 15, 7, 16, 11, 7, 14, 10, 13, 13, 8, 10, 11, 12, 6, 12, 10, 10, 10, 11, 5, 14, 8, 8, 5, 14, 6, 18, 13, 9, 13, 10, 4, 14, 12, 6, 11, 13, 12, 20, 11, 9, 13, 6, 12, 22, 13, 10, 10, 12, 5, 20, 11, 10, 11, 10, 11, 12, 11, 13, 12, 18, 7, 20, 15, 6, 8, 8, 8, 15, 12, 10, 14

Offset: 1

Author

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

Keywords

• base
• nonn

Examples

			a(2) = 8 since 13, 23, 31, 37, 43, 53, 73 and 83 are all primes.
a(3) = 9 since 233, 313, 331, 337, 353, 373, 383, 433 and 733 are all primes.
		

Links

• Michael De Vlieger and Robert G. Wilson v, Table of n, a(n) for n = 1..1215

Crossrefs

Cf. A265733, A266141, A266143, A266144, A266145, A266146, A266147, A266148, A266149, A055557, A099411.

Programs

Mathematica

f3[n_] := Block[{cnt = k = 0, r = 3 (10^n - 1)/9, s = Range[0, 9] - 3}, While[k < n, cnt += Length@ Select[r + 10^k*s, PrimeQ@ # && IntegerLength@ # > k &]; k++]; cnt]; Array[f3, 105]

PARI

a(n)={sum(i=0 ,n-1, sum(d=i==n-1, 9, isprime((10^n-1)/3 + (d-3)*10^i)))} \\ Andrew Howroyd, Feb 28 2018

Python

from _future_ import division
from sympy import isprime
def A266142(n):
    return 4*n if (n==1 or n==2) else sum(1 for d in range(-3,7) for i in range(n) if isprime((10**n-1)//3+d*10**i)) # Chai Wah Wu, Dec 27 2015

Extensions

a(2) corrected by Chai Wah Wu, Dec 27 2015

a(2) in b-file corrected as above by Andrew Howroyd, Feb 28 2018