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
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
Programs
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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
Comments