cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-8 of 8 results.

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

Views

Author

Vincenzo Librandi, Jun 06 2011

Keywords

Comments

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

Crossrefs

Cf. A014224, A059266, A059613, A059614, A095714, A177093.
Cf. A236371, A217131, A191469, A090669, A096305, A217130, A217132, A152213.

Programs

  • Magma
    [n: n in [1..1000]| IsPrime(7^n-6)]
  • Maple
    A191469:=n->`if`(isprime(7^n-6),n,NULL): seq(A191469(n), n=1..10^3); # Wesley Ivan Hurt, Nov 14 2014
  • Mathematica
    Select[Range[1,5000],PrimeQ[7^#-6]&] (* Vincenzo Librandi, Aug 05 2012 *)
  • PARI
    for(n=1, 10^6, if(isprime(7^n-6), print1(n, ", ")))

Extensions

a(17)-a(23) from Robert Price, Jan 24 2014
a(24) from Robert Price, Nov 14 2014

A145106 Numbers n such that 6^n+5 is prime.

Original entry on oeis.org

1, 2, 4, 7, 10, 14, 18, 32, 55, 102, 177, 190, 247, 276, 372, 1524, 1545, 2502, 4966, 5294, 13030, 13785, 14329, 27333, 44224, 93812, 127176, 128640, 136434, 184614, 269407, 311257, 349903, 389756
Offset: 1

Views

Author

Dmitry Kamenetsky, Oct 02 2008

Keywords

Comments

a(27) > 10^5. - Robert Price, Aug 06 2017
As reported by Lelio R Paula in November 2014 at primenumbers.net/prptop, the following three terms are also in this sequence: 127176, 128640, 136434. It is not confirmed that they are the next terms, however. - Robert Price, Aug 06 2017

Examples

			6^1+5=11 and 6^2+5=41, which are both prime, so 1 and 2 are in the sequence. 6^3+5=221 is not prime since it is divisible by 7, so 3 is not in the sequence.

Crossrefs

Cf. A059614.

Programs

Extensions

a(21)-a(26) from Robert Price, Aug 06 2017
a(27)-a(30) from Paul Bourdelais, Jan 28 2021
a(31)-a(34) from Paul Bourdelais, Feb 11 2021

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

Original entry on oeis.org

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

Views

Author

Vincenzo Librandi, Oct 02 2012

Keywords

Comments

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

Crossrefs

Cf. A059614, A217351.

Programs

  • Mathematica
    Select[Range[10000], PrimeQ[6^# - 7] &]
  • PARI
    is(n)=ispseudoprime(6^n-7) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

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

A217348 Numbers k such that 4^k - 5 is prime.

Original entry on oeis.org

2, 3, 4, 5, 6, 9, 10, 13, 16, 18, 28, 33, 59, 65, 75, 83, 103, 113, 275, 353, 405, 568, 614, 909, 1184, 1200, 1564, 2266, 2556, 4246, 8014, 8193, 8696, 9291, 10993, 12146, 13809, 15459, 16381, 24106, 60220, 91816, 158070, 182491, 207016, 266675, 297561
Offset: 1

Views

Author

Vincenzo Librandi, Oct 01 2012

Keywords

Examples

			28 is a term because 4^28 - 5 = 72057594037927931 is prime.

Crossrefs

Cf. A059266, A059608, A059614.

Programs

  • Mathematica
    Select[Range[10000], PrimeQ[4^# - 5] &]
  • PARI
    /* Up to 620 the code produces in few seconds the first terms: */
allocatemem(10000000); for(n=2, 620, if(isprime(4^n-5), print1(n", ")));

Formula

a(n) = A059608(n+1)/2. - Daniel Starodubtsev, Mar 20 2020

Extensions

a(31)-a(34) from Bruno Berselli, Oct 02 2012
a(35)-a(45) from Daniel Starodubtsev, Mar 20 2020
a(46)-a(47) derived from A059608 by Elmo R. Oliveira, Nov 28 2023

A182262 Least prime p that 6^n - p is prime.

Original entry on oeis.org

3, 5, 5, 5, 17, 7, 17, 7, 7, 7, 59, 19, 17, 13, 7, 19, 137, 13, 19, 7, 23, 97, 19, 89, 17, 223, 29, 109, 5, 19, 5, 59, 197, 5, 17, 307, 59, 83, 109, 157, 19, 23, 43, 109, 103, 7, 23, 19, 7, 269, 43, 13, 5, 67, 89, 83, 479, 53, 53, 383, 7, 83, 113, 37, 5, 23
Offset: 1

Views

Author

Mateusz Szymański, Apr 21 2012

Keywords

Examples

			For n=3 p=5 is the least prime that 6^3-p is prime (211).

Links

Crossrefs

Cf. A013607, A059614 (n such that a(n)=5).

Programs

  • Maple
    f:= proc(n) local t,p;
  t:= 6^n;
  p:= 2;
  do
    p:= nextprime(p);
  until isprime(t-p);
  p
end proc:
map(f, [$1..100]); # Robert Israel, Nov 05 2020
  • Mathematica
    f[n_] := Block[{p = 2}, While[! PrimeQ[6^n - p], p = NextPrime[p]];
  p]; Array[f, 60]
  • PARI
    a(n) = my(p = 2); while(!isprime(6^n-p), p = nextprime(p+1)); p; \\ Michel Marcus, Mar 23 2016

A290008 Prime numbers of the form 6^k - 5.

Original entry on oeis.org

31, 211, 1291, 36845653286788892983291, 1326443518324400147398651, 286511799958070431838109691, 174588755932389037098918153698611839369211, 380041719977839666236973721680871319659378770968571
Offset: 1

Views

Author

Robert Price, Sep 03 2017

Keywords

Links

Crossrefs

Cf. A059614.

Programs

  • Mathematica
    Select[Table[6^k - 5, {k, 1, 100}], PrimeQ[#] &]

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

Views

Author

Eric Chen, Jun 04 2018

Keywords

Comments

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.

Links

Crossrefs

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)).

Programs

  • PARI
    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

Views

Author

Daniel Starodubtsev, Aug 06 2019

Keywords

Comments

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

Examples

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

Crossrefs

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

Programs

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

Extensions

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
Showing 1-8 of 8 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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