A095714 -id:A095714 - cp's OEIS frontend

A108328 Integers n such that 10^n - 23 is a prime number.

3, 11, 17, 23, 35, 161, 765, 3473, 6887, 27681, 34313

Offset: 1

Julien Peter Benney (jpbenney(AT)ftml.net), Jun 30 2005

No additional terms < 40000. - Robert Price, Dec 13 2010
See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "99977".
No other terms < 100,000. - Robert Price, Mar 03 2011

			n = 3 is a member because 10^3 - 23 = 1000 - 23 = 977, which is prime.

Makoto Kamada, List of near-repdigit-related prime numbers.
Index entries for primes involving repunits.

Cf. A089675, A095714, A092767.

lst={};Do[If[PrimeQ[10^n-23], AppendTo[lst, n]], {n, 0, 10^4}];lst (* Vladimir Joseph Stephan Orlovsky, Aug 19 2008 *)

a(9)-a(11) from Robert Price, Dec 13 2010

Edited by Ray Chandler, Dec 23 2010

A108330 Integers k such that 10^k - 29 is a prime number.

Original entry on oeis.org

2, 3, 5, 7, 8, 13, 14, 761, 794, 2216, 3710, 3860, 3937, 5091, 7754, 29091

Offset: 1

Julien Peter Benney (jpbenney(AT)ftml.net), Jun 30 2005

The next term, if one exists, is > 100000. - Robert Price, Apr 25 2011

See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "99971".

			k = 8 is a term because 10^8 - 29 = 100000000 - 29 = 99999971, which is prime.

Makoto Kamada, List of near-repdigit-related prime numbers.
Index entries for primes involving repunits.

Cf. A089675, A095714, A092767.

a(14)-a(15) from Sean A. Irvine, Mar 04 2010
a(16) from Robert Price, Dec 15 2010
Edited by Ray Chandler, Dec 23 2010

A092767 Numbers k such that 10^k - 11 is prime.

Original entry on oeis.org

2, 5, 8, 12, 15, 18, 20, 30, 80, 143, 152, 164, 176, 239, 291, 324, 504, 594, 983, 2894, 22226, 35371, 58437, 67863, 180979

Offset: 1

Carl R. White, Apr 23 2004

Some of the larger terms may only correspond to probable primes.
The numbers corresponding to k = 324, 504, 594 & 983 are certified prime by Primo. - Robert G. Wilson v, Jul 01 2005
a(26) > 2.5*10^5. - Robert Price, Apr 12 2015

			k = 5 is a term because 10^5 - 11 = 100000 - 11 = 99989, which is prime.

Makoto Kamada, Near-repdigit numbers of the form AA...AABA.
Makoto Kamada, Prime numbers of the form 99...9989.
Index entries for primes involving repunits.

Cf. A089675, A086865, A004023, A095714.

Do[ If[ PrimeQ[10^n - 11], Print[n]], {n, 3000}] (* Robert G. Wilson v, Jul 01 2005 *)

for(n=0,5000,if(isprime(10^n-11),print1(n,","))) \\ Ryan Propper, Jun 15 2005

4 more terms from Ryan Propper, Jun 15 2005
Edited by N. J. A. Sloane, May 04 2007
a(21)-a(22) from Robert Price, Dec 12 2010
Edited by Ray Chandler, Dec 23 2010
a(23)=58437 and a(24)=67863 from Robert Price, May 29 2011
a(25) from Kamada data by Robert Price, Apr 12 2015

A266148 Number of n-digit primes in which n-1 of the digits are 9's.

Original entry on oeis.org

4, 6, 7, 7, 8, 10, 7, 13, 8, 8, 11, 13, 8, 11, 13, 14, 10, 9, 7, 11, 9, 13, 10, 19, 5, 10, 14, 7, 10, 9, 9, 15, 13, 8, 7, 9, 10, 11, 10, 13, 5, 12, 15, 7, 12, 7, 12, 11, 13, 11, 8, 13, 13, 13, 12, 12, 9, 9, 15, 14, 9, 8, 13, 11, 15, 17, 10, 8, 11, 10, 6, 16, 8, 8, 8, 15, 9, 11, 14, 7, 10, 11, 16, 17, 11, 10, 12, 16, 8, 15, 7, 11, 11, 10, 7, 12, 6, 10, 8, 9

Offset: 1

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

The other digit cannot be 0, 3, 6, or 9, or else the number would not be prime. - N. J. A. Sloane, May 20 2016

			a(3) = 7 since 199, 499, 599, 919, 929, 991 and 997 are all the three-digit primes containing two 9's.

Dana Jacobsen, Table of n, a(n) for n = 1..2500 (first 1215 terms from Michael De Vlieger and Robert G. Wilson v)

Cf. A265733, A266141, A266142, A266143, A266144, A266145, A266146, A266147, A266149, A095714, A089675.

f9[n_] := Block[{cnt = k = 0, r = 9 (10^n - 1)/9, s = Range[0, 9] - 9}, While[k < n, cnt += Length@ Select[r + 10^k * s, PrimeQ@ # && IntegerLength@ # > k &]; k++]; cnt]; Array[f9, 100]

use ntheory ":all"; sub a266148 { my $n = shift; vecsum( map { my $k=$; scalar grep { is_prime("9" x $k . $ . "9" x ($n-$k-1)) } 0+($k>0) .. 8 } 0 .. $n-1 ); } # Dana Jacobsen, Jan 01 2016

from sympy import isprime
def A266148(n):
    return sum(1 for d in range(-9,1) for i in range(n) if isprime(10**n-1+d*10**i)) # Chai Wah Wu, Dec 31 2015

A191469 Numbers n such that 7^n - 6 is prime.

Original entry on oeis.org

2, 3, 6, 9, 21, 25, 33, 49, 54, 133, 245, 255, 318, 1023, 1486, 3334, 6821, 8555, 11605, 42502, 44409, 90291, 92511, 140303

Offset: 1

Vincenzo Librandi, Jun 06 2011

a(14)=1023 and a(15)=1486 correspond to BPSW strong probable primes (passing PARI's ispseudoprime()). - Joerg Arndt, Jun 06 2011

a(25) > 2*10^5. - Robert Price, Nov 14 2014

Cf. A014224, A059266, A059613, A059614, A095714, A177093.

Cf. A236371, A217131, A191469, A090669, A096305, A217130, A217132, A152213.

Magma
```
[n: n in [1..1000]| IsPrime(7^n-6)]
```

A191469:=n->`if`(isprime(7^n-6),n,NULL): seq(A191469(n), n=1..10^3); # Wesley Ivan Hurt, Nov 14 2014

Select[Range[1,5000],PrimeQ[7^#-6]&] (* Vincenzo Librandi, Aug 05 2012 *)

for(n=1, 10^6, if(isprime(7^n-6), print1(n, ", ")))

a(17)-a(23) from Robert Price, Jan 24 2014

a(24) from Robert Price, Nov 14 2014

A093177 Primes of the form 90*R_k + 1, where R_k is the repunit (A002275) of length k.

Original entry on oeis.org

991, 99991, 9999991, 999999999999999999999999999999991, 999999999999999999999999999999999999999999991, 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991

Offset: 1

Rick L. Shepherd, Mar 27 2004

nonn

Primes of the form 10^k - 9 (k=3,5,7,...). - Vincenzo Librandi, Nov 16 2010

Makoto Kamada, Prime numbers of the form 99...991.
Index entries for primes involving repunits

Cf. A056696 (corresponding k), A095714.

a(n) = 10^(A056696(n)+1) - 9 = 10^A095714(n) - 9.

Edited by Ray Chandler, Feb 26 2012

A108506 Integers n such that 10^n-59 is prime.

Original entry on oeis.org

2, 3, 4, 8, 20, 38, 95, 248, 263, 303, 304, 410, 438, 548, 688, 1074, 1575, 8364, 9910, 15910, 37344

Offset: 1

Julien Peter Benney (jpbenney(AT)ftml.net), Jul 06 2005

Certified primality of numbers corresponding to terms 410, 438, 548, 688, 1074 and 1575 with Primo. - Ryan Propper, Jul 08 2005
No other terms <40000.
See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "99941".

			8 is a member because: n = 8 gives 10^8-59 = 100000000-59 = 99999941, which is prime.

Makoto Kamada, List of near-repdigit-related prime numbers.
Index entries for primes involving repunits.

Cf. A089675, A095714, A092767, A108327, A108328, A108329, A108330, A108331, A108332, A177418.

a(18)-a(20) from Kamada data by Robert Price, Dec 10 2010
a(21) by Robert Price, Dec 16 2010
Edited by Ray Chandler, Dec 23 2010

A056696 Numbers k such that 90*R_k + 1 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

Original entry on oeis.org

2, 4, 6, 32, 44, 104, 196, 198, 280, 300, 316, 1106, 1656, 3394, 35924, 37596, 64304, 80138, 221630

Offset: 1

Robert G. Wilson v, Aug 10 2000

nonn

Also numbers k such that 10^(k+1) - 9 is a prime.

Makoto Kamada, Prime numbers of the form 99...991.
Index entries for primes involving repunits

Cf. A002275, A093177, A095714.

Do[ If[ PrimeQ[90*(10^n - 1)/9 + 1], Print[n]], {n, 0, 7000}]

a(n) = A095714(n) - 1.

a(15) - a(16) from Jason Earls, Jan 07 2008
a(17) - a(19) from Alexander Gramolin, May 13 2011
Edited by Ray Chandler, Feb 26 2012

A108327 Integers n such that 10^n-21 is a prime number.

Original entry on oeis.org

2, 6, 32, 108, 408, 1286, 2268, 2328, 4284, 53558, 181182, 249010

Offset: 1

Julien Peter Benney (jpbenney(AT)ftml.net), Jun 30 2005

a(13) > 2.5*10^5. - Robert Price, Apr 12 2015

			6 is a member because 10^6-21 = 1000000-21 = 999979, which is prime.

Makoto Kamada, Near-repdigit numbers of the form AA...AABA.
Makoto Kamada, Prime numbers of the form 99...9979.
Index entries for primes involving repunits.

Cf. A089675, A095714, A092767.

Edited by Ray Chandler, Dec 23 2010
a(10)=53558 from Robert Price, Mar 03 2011
a(11)-a(12) from Kamada data by Robert Price, Apr 12 2015

A108329 Integers k such that 10^k - 27 is prime.

Original entry on oeis.org

2, 4, 7, 14, 20, 22, 29, 31, 40, 80, 85, 224, 767, 952, 3592, 4016, 4187, 9239, 17684, 20716, 30791

Offset: 1

Julien Peter Benney (jpbenney(AT)ftml.net), Jun 30 2005

See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "99973".

The next term, if one exists, is > 100000. - Robert Price, Apr 25 2011

			k = 7 is a term because 10^7 - 27 = 10000000 - 27 = 9999973, which is prime.

Makoto Kamada, List of near-repdigit-related prime numbers.
Index entries for primes involving repunits.

Cf. A089675, A095714, A092767, A176987.

a(18)-a(19) from Kamada data by Robert Price, Dec 10 2010
a(20)-a(21) from Robert Price, Dec 15 2010
Edited by Ray Chandler, Dec 23 2010

cp's OEIS Frontend

A108328 Integers n such that 10^n - 23 is a prime number.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Extensions

A108330 Integers k such that 10^k - 29 is a prime number.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions

A092767 Numbers k such that 10^k - 11 is prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A266148 Number of n-digit primes in which n-1 of the digits are 9's.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Perl

Python

A191469 Numbers n such that 7^n - 6 is prime.

Views

Author

Keywords

Comments

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Extensions

A093177 Primes of the form 90*R_k + 1, where R_k is the repunit (A002275) of length k.

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

Extensions

A108506 Integers n such that 10^n-59 is prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions

A056696 Numbers k such that 90*R_k + 1 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

Views

Author

Keywords

Comments