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

1,1

Links

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

Example

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.

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]

Prog

(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

Crossrefs

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

Sequence in context: A368812 A229004 A306976 * A297252 A296696 A297129

Adjacent sequences: A266139 A266140 A266141 * A266143 A266144 A266145

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

Status

approved