A266146 Number of n-digit primes in which n-1 of the digits are 7's.

4, 8, 10, 9, 12, 11, 8, 4, 9, 9, 10, 14, 14, 11, 16, 7, 10, 17, 7, 10, 9, 12, 9, 13, 11, 10, 14, 5, 3, 22, 6, 13, 13, 10, 8, 16, 8, 6, 16, 8, 13, 14, 8, 7, 8, 13, 9, 11, 13, 9, 14, 8, 4, 23, 13, 11, 8, 8, 8, 12, 13, 13, 11, 11, 10, 23, 11, 8, 8, 3, 6, 16, 12, 13, 12, 12, 8, 11, 8, 11, 14, 13, 7, 15, 12, 17, 11, 7, 9, 21, 6, 6, 11, 12, 6, 14, 14, 12, 13, 12, 11, 17, 10, 17, 18

Offset: 1

Author

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

Keywords

• base
• nonn

Examples

			a(2) = 8 from 17, 37, 47, 67, 71, 73, 79, 97. - _N. J. A. Sloane_, Dec 27 2015
a(3) = 10 since 277, 577, 677, 727, 757, 773, 787, 797, 877, and 977 are primes.
		

Links

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

Crossrefs

Cf. A265733, A266141, A266142, A266143, A266144, A266145, A266147, A266148, A266149, A099419, A099420, A098089.

Programs

Mathematica

f7[n_] := Block[{cnt = k = 0, r = 7 (10^n - 1)/9, s = Range[0, 9] - 7}, While[k < n, cnt += Length@ Select[r + 10^k*s, PrimeQ@ # && IntegerLength@ # > k &]; k++]; cnt]; Array[f7, 100]

PARI

a(n)={sum(i=0, n-1, sum(d=i==n-1, 9, isprime((10^n-1)/9*7 + (d-7)*10^i)))} \\ Andrew Howroyd, Feb 28 2018

Python

from _future_ import division
from sympy import isprime
def A266146(n):
     return 4*n if (n==1 or n==2) else sum(1 for d in range(-7,3) for i in range(n) if isprime(7*(10**n-1)//9+d*10**i)) # Chai Wah Wu, Dec 27 2015

Extensions

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

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