A099415 -id:A099415 - cp's OEIS frontend

A266144 Number of n-digit primes in which n-1 of the digits are 5's.

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

Offset: 1

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

The leading digits must be 5's and only the trailing digit can vary.

For n large a(n) is usually zero.

			a(2) = 2 since 53 and 59 are primes.
a(3) = 1 since 557 is the only prime.

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

Cf. A265733, A266141, A266142, A266143, A266145, A266146, A266147, A266148, A266149, A099415, A099416, A099417, A099418.

d = 5; Array[Length@ Select[d (10^# - 1)/9 + (Range[0, 9] - d), PrimeQ] &, 100]

from _future_ import division
from sympy import isprime
def A266144(n):
    return 4 if n==1 else sum(1 for d in [-4,-2,2,4] if isprime(5*(10**n-1)//9+d)) # Chai Wah Wu, Dec 27 2015

A056684 Numbers k such that 50*R_k + 1 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

Original entry on oeis.org

11, 12, 608

Offset: 1

Robert G. Wilson v, Aug 10 2000

Also numbers k such that (5*10^(k+1)-41)/9 is prime.

a(4) > 10^5. - Robert Price, Nov 16 2014

Makoto Kamada, Prime numbers of the form 55...551.
Index entries for primes involving repunits

Cf. A002275, A099415.

Do[ If[ PrimeQ[50*(10^n - 1)/9 + 1], Print[n]], {n, 15000}]

a(n) = A099415(n) - 1. - Robert Price, Nov 16 2014

cp's OEIS Frontend

A266144 Number of n-digit primes in which n-1 of the digits are 5's.

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