A095714 -id:A095714 - cp's OEIS frontend

A108331 Integers k such that 10^k - 87 is prime.

2, 1800, 2368, 15328

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 "99913".

a(5) > 10^5. - Tyler NeSmith, Jul 26 2021

			k = 2 is a term because 10^2 - 87 = 100 - 87 = 13, which is prime.

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

Cf. A089675, A095714, A092767.

a(4) from Kamada data by Robert Price, Dec 13 2010

Edited by Ray Chandler, Dec 23 2010

A108332 Integers k such that 10^k - 89 is prime.

Original entry on oeis.org

2, 3, 637, 2349, 29455, 175093

Offset: 1

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

637 corresponds to a certified prime (Primo 2.2.0 beta). - Ryan Propper, Nov 06 2005
No additional terms < 40000.
See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "9w11".

			k = 3 is a term because 10^3 - 89 = 1000 - 89 = 911, which is prime.

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

Cf. A089675, A095714, A092767.

Do[If[PrimeQ[10^n - 89], Print[n]], {n, 2, 10^4}] (* Ryan Propper, Nov 06 2005 *)

a(5) from Robert Price, Dec 15 2010
Edited by Ray Chandler, Dec 23 2010
a(6) from Riley Fisher, Oct 09 2023

A101396 Numbers k such that 4*10^k - 9 is prime.

Original entry on oeis.org

1, 17, 19, 29, 43, 119, 173, 949, 1609, 5579, 19679, 34147, 43493, 97799

Offset: 1

Julien Peter Benney (jpbenney(AT)ftml.net), Jan 15 2005

a(15) > 10^5. - Robert Price, Mar 17 2015

All terms are odd, since 4 * 10^(2*k) - 9 = (2 * 10^k - 3)*(2 * 10^k + 3). - Robert Israel, Mar 17 2015

			n = 1, 17, 19 are members since 31, 399999999999999991 and 39999999999999999991 are primes.

Makoto Kamada, Prime numbers of the form 399...991.
Index entries for primes involving repunits.

Cf. A095714, A101848.

[n: n in [1..300] |IsPrime(4*10^n - 9)]; // Vincenzo Librandi, Mar 18 2015

select(n -> n::odd and isprime(4*10^n-9), [$1..10000]); # Robert Israel, Mar 17 2015

Do[ If[ PrimeQ[4*10^n - 9], Print[n]], {n, 0, 10000}]

is(n)=ispseudoprime(4*10^n-9) \\ Charles R Greathouse IV, Jun 12 2017

a(n) = A101848(n) + 1.

a(11) from Kamada link by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

a(12)-a(14) from Kamada data by Robert Price, Mar 17 2015

A108493 Integers n such that 10^n-57 is prime.

Original entry on oeis.org

2, 7, 10, 11, 17, 19, 39, 49, 50, 61, 95, 106, 187, 196, 849, 889, 6436, 7370, 14446, 19647, 34399, 39922, 81297, 84305

Offset: 1

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

Numbers corresponding to terms 849 and 889 are certified primes. (Primo 2.2.0 beta) - Ryan Propper, Jul 13 2005
No additional terms <100000.
See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "99943".

			n = 7 is a member because: 10^7-57 = 10000000-57 = 9999943, 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, A177417.

a(17)-a(19) from Kamada data by Robert Price, Dec 10 2010
a(20) from Kamada data by Robert Price, Dec 14 2010
a(21)-a(22) from Robert Price, Dec 15 2010
Edited by Ray Chandler, Dec 23 2010
a(23-24)=81297,84305 from Robert Price, May 29 2011

A305531 Smallest k >= 1 such that (n-1)*n^k + 1 is prime.

Original entry on oeis.org

1, 1, 1, 2, 1, 1, 2, 1, 3, 10, 3, 1, 2, 1, 1, 4, 1, 29, 14, 1, 1, 14, 2, 1, 2, 4, 1, 2, 4, 5, 12, 2, 1, 2, 2, 9, 16, 1, 2, 80, 1, 2, 4, 2, 3, 16, 2, 2, 2, 1, 15, 960, 15, 1, 4, 3, 1, 14, 1, 6, 20, 1, 3, 946, 6, 1, 18, 10, 1, 4, 1, 5, 42, 4, 1, 828, 1, 1, 2, 1, 12, 2, 6, 4, 30, 3, 3022, 2, 1, 1

Offset: 2

Eric Chen, Jun 04 2018

nonn

a(prime(j)) + 1 = A087139(j).
a(123) > 10^5, a(342) > 10^5, see the Barnes link for the Sierpinski base-123 and base-342 problems.
a(251) > 73000, see A087139.

Eric Chen, Table of n, a(n) for n = 2..122
Gary Barnes, Sierpinski conjectures and proofs
Eric Chen, Table n, a(n) for n = 2..360 status

For the numbers k such that these forms are prime:
a1(b): numbers k such that (b-1)*b^k-1 is prime
a2(b): numbers k such that (b-1)*b^k+1 is prime
a3(b): numbers k such that (b+1)*b^k-1 is prime
a4(b): numbers k such that (b+1)*b^k+1 is prime (no such k exists when b == 1 (mod 3))
a5(b): numbers k such that b^k-(b-1) is prime
a6(b): numbers k such that b^k+(b-1) is prime
a7(b): numbers k such that b^k-(b+1) is prime
a8(b): numbers k such that b^k+(b+1) is prime (no such k exists when b == 1 (mod 3)).
Using "-------" if there is currently no OEIS sequence and "xxxxxxx" if no such k exists (this occurs only for a4(b) and a8(b) for b == 1 (mod 3)):
.
   b   a1(b)   a2(b)   a3(b)   a4(b)   a5(b)   a6(b)   a7(b)   a8(b)
--------------------------------------------------------------------
   2 A000043 ------- A002235 A002253 A000043 ------- A050414 A057732
   3 A003307 A003306 A005540 A005537 A014224 A051783 A058959 A058958
   4 A272057 ------- ------- xxxxxxx A059266 A089437 A217348 xxxxxxx
   5 A046865 A204322 A257790 A143279 A059613 A124621 A165701 A089142
   6 A079906 A247260 ------- ------- A059614 A145106 A217352 A217351
   7 A046866 A245241 ------- xxxxxxx A191469 A217130 A217131 xxxxxxx
   8 A268061 A269544 ------- ------- A217380 A217381 A217383 A217382
   9 A268356 A056799 ------- ------- A177093 A217385 A217493 A217492
  10 A056725 A056797 A111391 xxxxxxx A095714 A088275 A092767 xxxxxxx
  11 A046867 A057462 ------- ------- ------- ------- ------- -------
  12 A079907 A251259 ------- ------- ------- A137654 ------- -------
  13 A297348 ------- ------- xxxxxxx ------- ------- ------- xxxxxxx
  14 A273523 ------- ------- ------- ------- ------- ------- -------
  15 ------- ------- ------- ------- ------- ------- ------- -------
  16 ------- ------- ------- xxxxxxx ------- ------- ------- xxxxxxx
Cf. (smallest k such that these forms are prime) A122396 (a1(b)+1 for prime b), A087139 (a2(b)+1 for prime b), A113516 (a5(b)), A076845 (a6(b)), A178250 (a7(b)).

a(n)=for(k=1,2^16,if(ispseudoprime((n-1)*n^k+1),return(k)))

A108326 Integers n such that 10^n-17 is prime.

Original entry on oeis.org

2, 3, 6, 30, 40, 86, 128, 264, 639, 912, 1932, 4650, 5038, 7410, 19041

Offset: 1

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

Terms 639 and 912 correspond to certified primes (Primo 2.2.0 beta). - Ryan Propper, Jul 12 2005
No other terms < 40000.
See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "99983".
No other terms < 100,000. - Robert Price, Mar 03 2011

			If n = 3 we have 10^3-17 = 1000-17 = 983, 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 Robert Price, Dec 11 2010

Edited by Ray Chandler, Dec 23 2010

cp's OEIS Frontend

A108331 Integers k such that 10^k - 87 is prime.

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A108332 Integers k such that 10^k - 89 is prime.

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A101396 Numbers k such that 4*10^k - 9 is prime.

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A108493 Integers n such that 10^n-57 is prime.

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A305531 Smallest k >= 1 such that (n-1)*n^k + 1 is prime.

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PARI

A108326 Integers n such that 10^n-17 is prime.

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