A089142 -id:A089142 - cp's OEIS frontend

A217133 Numbers n such that 5^n + 8 is prime.

1, 95, 335, 3155, 28651, 91135

Offset: 1

Vincenzo Librandi, Oct 01 2012

Naturally these numbers are odd since (6-1)^(2n)+8 is divisible by 3. - Bruno Berselli, Oct 04 2012
a(7) > 10^5. - Robert Price, Feb 03 2014
a(7) > 5*10^5. - Tyler NeSmith, Apr 24 2022

Cf. A087885, A089142, A124621.

Select[Range[1, 15000, 2], PrimeQ[5^# + 8] &]

for(n=1, 5*10^3, if(isprime(5^n+8), print1(n", ")))

a(5)-a(6) from Robert Price, Feb 03 2014

A228029 Primes of the form 5^n + 6.

Original entry on oeis.org

7, 11, 31, 131, 631, 1220703131

Offset: 1

Vincenzo Librandi, Aug 11 2013

Vincenzo Librandi, Table of n, a(n) for n = 1..15

Cf. A089142 (associated n).

Cf. Primes of the form k^n + h: A092506 (k=2, h=1), A057733 (k=2, h=3), A123250 (k=2, h=5), A104066 (k=2, h=7), A104070 (k=2, h=9), A057735 (k=3, h=2), A102903 (k=3, h=4), A102870 (k=3, h=8), A102907 (k=3, h=10), A290200 (k=4, h=1), A182330 (k=5, h=2), this sequence (k=5, h=6), A102910 (k=5, h=8), A182331 (k=6, h=1), A104118 (k=6, h=5), A104115 (k=6, h=7), A104065 (k=7, h=4), A144360 (k=8, h=7), A145440 (k=8, h=9), A228034 (k=9, h=2), A159352 (k=10, h=3), A159031 (k=10, h=7).

[a: n in [0..200] | IsPrime(a) where a is  5^n+6];

Select[Table[5^n + 6, {n, 0, 200}], PrimeQ]

Corrected cross-references - Robert Price, Aug 01 2017

A217134 Numbers n such that 5^n - 8 is prime.

Original entry on oeis.org

2, 4, 10, 14, 88, 112, 140, 764, 3040, 11096, 24934, 25616, 54584, 93400

Offset: 1

Vincenzo Librandi, Oct 01 2012

nonn

a(15) > 10^5. - Robert Price, Feb 03 2014

Cf. A059613, A087885, A089142, A109080, A124621, A165701.

Select[Range[2, 5000], PrimeQ[5^# - 8] &]

for(n=2, 5*10^3, if(isprime(5^n-8), print1(n", ")))

a(10)-a(14) from Robert Price, Feb 03 2014

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)))

A378815 Numbers k such that 5^k + 64 is prime.

Original entry on oeis.org

2, 58, 170, 1402, 1774, 10802, 86342

Offset: 1

Robert Price, Dec 08 2024

			2 is a term because 5^2 + 64 = 89 is prime.

Cf. A089142, A124621, A217133.

Magma
```
[k: k in [0..1000] |IsPrime (5^k+64)];
```
Mathematica
```
Select[Range[0,5000],PrimeQ[5^#+64]&]
```

a(6) from Michael S. Branicky, Dec 17 2024

a(7) from Michael S. Branicky, Dec 23 2024

A378832 Numbers k such that 5^k + 68 is prime.

Original entry on oeis.org

1, 3, 7, 133, 331, 453, 10365

Offset: 1

Robert Price, Dec 08 2024

a(8) > 22000. - Matthew L. LaSelle, Feb 25 2025

a(8) > 100000. - Michael S. Branicky, Mar 28 2025

			3 is a term because 5^3 + 68 = 193 is prime.

Cf. A089142, A124621, A217133.

Magma
```
[k: k in [0..1000] |IsPrime (5^k+68)];
```
Mathematica
```
Select[Range[0,5000],PrimeQ[5^#+68]&]
```

a(7) from Michael S. Branicky, Dec 17 2024

A378866 Numbers k such that 5^k + 72 is prime.

Original entry on oeis.org

0, 2, 3, 118, 498, 1023, 4262, 6094, 6382, 26334, 56062

Offset: 1

Robert Price, Dec 09 2024

			3 is a term because 5^3 + 72 = 197 is prime.

Cf. A089142, A124621, A217133.

Magma
```
[k: k in [0..1000] |IsPrime (5^k+72)];
```
Mathematica
```
Select[Range[0,5000],PrimeQ[5^#+72]&]
```

a(8)-a(11) from Michael S. Branicky, Dec 19 2024

A378867 Numbers k such that 5^k + 86 is prime.

Original entry on oeis.org

3, 27, 179, 507, 4671, 4923, 5871, 7571, 19551, 19955

Offset: 1

Robert Price, Dec 09 2024

a(11) > 10^5. - Michael S. Branicky, Dec 22 2024

			3 is a term because 5^3 + 86 = 211 is prime.

Cf. A089142, A124621, A217133.

Magma
```
[k: k in [0..1000] |IsPrime (5^k+86)];
```
Mathematica
```
Select[Range[0,5000],PrimeQ[5^#+86]&]
```

a(5)-a(10) from Vincenzo Librandi, Dec 17 2024

cp's OEIS Frontend

A217133 Numbers n such that 5^n + 8 is prime.

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A228029 Primes of the form 5^n + 6.

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A217134 Numbers n such that 5^n - 8 is prime.

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

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PARI

A378815 Numbers k such that 5^k + 64 is prime.

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Magma

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A378832 Numbers k such that 5^k + 68 is prime.

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Magma

Mathematica

Extensions

A378866 Numbers k such that 5^k + 72 is prime.

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Keywords

Examples

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Programs

Magma

Mathematica

Extensions

A378867 Numbers k such that 5^k + 86 is prime.

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Author

Keywords

Comments

Examples

Crossrefs

Programs

Magma