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

1,1

Links

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

Example

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.

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]

Prog

(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

Crossrefs

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

Sequence in context: A261602 A377034 A265733 * A329503 A108806 A310967

Adjacent sequences: A266143 A266144 A266145 * A266147 A266148 A266149

Keyword

base,nonn

Author

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

Status

approved