A099409 -id:A099409 - cp's OEIS frontend

A266141 Number of n-digit primes in which n-1 of the digits are 2's.

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

Offset: 1

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

The leading digits must be 2's and only the trailing digit can vary.
For n large a(n) is usually zero.
a(n) <= 4.  If n > 1 and not a multiple of 3, then a(n) <= 2.  It appears that a(n) <= 1 for n > 3. - Chai Wah Wu, Dec 26 2015

			a(3) = 3 since 223, 227 and 229 are all primes.

Dana Jacobsen, Table of n, a(n) for n = 1..10000 (first 1500 terms from Michael De Vlieger and Robert G. Wilson v)

Cf. A265733, A266142, A266143, A266144, A266145, A266146, A266147, A266148, A266149, A084832, A096506, A099409, A099410.

d = 2; Array[Length@ Select[d (10^# - 1)/9 + (Range[0, 9] - d), PrimeQ] &, 100]

use ntheory ":all"; sub a266141 { my $n=shift; return 4 if $n==1; 0+scalar(grep{is_prime("2"x($n-1).$)} 1,3,7,9); } say a266141($) for 1..20; # Dana Jacobsen, Dec 27 2015

from sympy import isprime
def A266141(n):
    return 4 if n==1 else sum(1 for d in '1379' if isprime(int('2'*(n-1)+d))) # Chai Wah Wu, Dec 26 2015

A056677 Numbers k such that 20*R_k + 7 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

Original entry on oeis.org

0, 2, 8, 14, 27, 63, 1167, 1694, 2361, 116619

Offset: 1

Robert G. Wilson v, Aug 10 2000

Also numbers k such that (2*10^(k+1)+43)/9 is prime.

Makoto Kamada, Prime numbers of the form 22...227.
Index entries for primes involving repunits

Cf. A002275, A093167, A099409.

Do[ If[ PrimeQ[20*(10^n - 1)/9 + 7], Print[n]], {n, 0, 5000}]
Flatten[Position[Table[FromDigits[PadLeft[{7},n,2]],{n,5000}], ?PrimeQ]]-1 (* _Harvey P. Dale, May 01 2012 *)
Select[Range[0, 2500], PrimeQ[20*(10^n - 1)/9 + 7]&] (* Mikk Heidemaa, Nov 28 2015 *)

a(n) = A099409(n+1) - 1. - Robert Price, Jan 30 2015

a(10) from Kamada link entered by Michael S. Branicky, Jan 14 2023

A093167 Primes of the form 20*R_k + 7, where R_k is the repunit (A002275) of length k.

Original entry on oeis.org

7, 227, 222222227, 222222222222227, 2222222222222222222222222227, 2222222222222222222222222222222222222222222222222222222222222227

Offset: 1

Rick L. Shepherd, Mar 26 2004

Makoto Kamada, Prime numbers of the form 22...227.
Index entries for primes involving repunits

Cf. A002275, A056677 (corresponding k and count of digits 2 in a(n)), A099409.

Select[FromDigits /@ NestList["2" <> # &, "7", 10^3], PrimeQ] (* Mikk Heidemaa, Nov 18 2015 *)

list(lim)=for(i=0,lim,m=20*(10^i-1)/9 + 7;if(isprime(m),print1(m," ,"))) \\ Anders Hellström, Nov 18 2015

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A266141 Number of n-digit primes in which n-1 of the digits are 2's.

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A056677 Numbers k such that 20*R_k + 7 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

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A093167 Primes of the form 20*R_k + 7, where R_k is the repunit (A002275) of length k.

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