A099413 -id:A099413 - cp's OEIS frontend

A266143 Number of n-digit primes in which n-1 of the digits are 4's.

4, 3, 2, 2, 1, 2, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

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

The leading digits must be 4's and only the trailing digit can vary.

For n large a(n) is usually zero.

			a(3) = 2 since 443 and 449 are primes.
a(4) = 2 since 4441 and 4447 are primes.

Michael De Vlieger and Robert G. Wilson v, Table of n, a(n) for n = 1..1500

Cf. A265733, A266141, A266142, A266144, A266145, A266146, A266147, A266148, A266149, A099412, A096845, A099413, A099414.

d = 4; Array[Length@ Select[d (10^# - 1)/9 + (Range[0, 9] - d), PrimeQ] &, 100]

from _future_ import division
from sympy import isprime
def A266143(n):
    return 4 if n==1 else sum(1 for d in [-3,-1,3,5] if isprime(4*(10**n-1)//9+d)) # Chai Wah Wu, Dec 27 2015

A056682 Numbers k such that 40*R_k + 7 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

Original entry on oeis.org

0, 1, 3, 9, 19, 25, 721, 1309, 3169, 28933, 66283, 67795

Offset: 1

Robert G. Wilson v, Aug 10 2000

Also numbers k such that (4*10^(k+1)+23)/9 is prime.

a(13) > 10^5. - Robert Price, Nov 30 2014

Makoto Kamada, Prime numbers of the form 44...447.
Index entries for primes involving repunits

Cf. A002275, A099413.

Do[ If[ PrimeQ[40*(10^n - 1)/9 + 7], Print[n]], {n, 0, 5000}]

a(n) = A099413(n+1)-1. - Robert Price, Nov 30 2014

a(10)-a(12) derived from A099413 by Robert Price, Nov 30 2014

cp's OEIS Frontend

A266143 Number of n-digit primes in which n-1 of the digits are 4's.

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