A217351 -id:A217351 - cp's OEIS frontend

A217352 Numbers k such that 6^k - 7 is prime.

2, 4, 6, 8, 9, 10, 15, 20, 46, 49, 61, 98, 110, 144, 266, 344, 978, 1692, 1880, 1924, 3142, 3220, 4209, 5708, 7064, 13465, 13858, 19474, 22666, 26807

Offset: 1

Vincenzo Librandi, Oct 02 2012

a(31) > 50000. - Michael S. Branicky, Oct 27 2024

Cf. A059614, A217351.

Mathematica
```
Select[Range[10000], PrimeQ[6^# - 7] &]
```

is(n)=ispseudoprime(6^n-7) \\ Charles R Greathouse IV, Jun 13 2017

a(26)-a(27) from Michael S. Branicky, Jan 29 2023
a(28)-a(29) from Michael S. Branicky, Apr 10 2023
a(30) from Michael S. Branicky, Oct 27 2024

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)))

A309527 Numbers k such that 6^k + 17 is prime.

Original entry on oeis.org

1, 2, 3, 5, 8, 10, 19, 27, 79, 198, 565, 787, 2183, 3811, 4748, 6210, 7887, 8965, 13303, 20125, 23433, 28797

Offset: 1

Daniel Starodubtsev, Aug 06 2019

a(20) > 14000. - Daniel Starodubtsev, Apr 17 2020

			3 is in the sequence because 6^3 + 17 = 233, which is prime.

Cf. A013600, A013607, A059614, A145106, A182331, A217351, A217352.

lista(nn)=for(k=0,nn,if(ispseudoprime(6^k+17),print1(k", ")))

a(17)-a(18) from Daniel Starodubtsev, Mar 16 2020
a(19) from Daniel Starodubtsev, Apr 17 2020
a(20)-a(22) from Michael S. Branicky, Mar 14 2023

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A217352 Numbers k such that 6^k - 7 is prime.

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

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A309527 Numbers k such that 6^k + 17 is prime.

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