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
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
Programs
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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
Comments