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 1-5 of 5 results.

A079906 Numbers k such that 5*6^k - 1 is prime.

Original entry on oeis.org

1, 2, 6, 7, 11, 23, 33, 48, 68, 79, 116, 151, 205, 1016, 1332, 1448, 3481, 3566, 3665, 11233, 13363, 29166, 44358, 58530, 191706, 386450, 605168, 616879, 1204077
Offset: 1

Views

Author

Robert G. Wilson v, Jan 16 2003

Keywords

Comments

a(29) > 618000. - Karsten Bonath, Nov 04 2019

References

  • R. K. Guy, Unsolved Problems in Theory of Numbers, Section A3.

Links

Crossrefs

Cf. A003307, A002235, A046865, A046866, A001771, A005541, A056725, A046867, A079907, A247260.

Programs

  • Mathematica
    Do[ If[ PrimeQ[5*6^n - 1], Print[n]], {n, 1, 5000}]
  • PARI
    for(n=1,2000, if(isprime(5*6^n-1),print1(n, ", ")))

Extensions

a(20)-a(24) from Donovan Johnson, Nov 26 2008
a(25) from Robert Price, Jan 23 2016
a(26) from Karsten Bonath, Jul 01 2019
a(27) from Karsten Bonath, Oct 29 2019
a(28) from Karsten Bonath, Nov 04 2019
a(29) from Ryan Propper, Nov 21 2023

A268061 Numbers k such that 7*8^k - 1 is prime.

Original entry on oeis.org

3, 7, 15, 59, 6127, 8703, 11619, 23403, 124299
Offset: 1

Views

Author

Robert Price, Jan 25 2016

Keywords

Comments

a(10) > 2*10^5.
Terms are A001771(n)/3 that are integers.

References

  • R. K. Guy, Unsolved Problems in Theory of Numbers, Section A3.

Links

Crossrefs

Cf. similar sequences of the form k*(k+1)^n-1: A003307 (k=2), ... (k=3), A046865 (k=4), A079906 (k=5), A046866 (k=6), this sequence (k=7), ... (k=8), A056725 (k=9), A046867 (k=10), A079907 (k=11).
Cf. A001771, A002235, A005541, A247260.

Programs

  • Mathematica
    Select[Range[0, 200000], PrimeQ[7*8^# - 1] &]
  • PARI
    lista(nn) = for(n=1, nn, if(ispseudoprime(7*8^n-1), print1(n, ", "))) \\ Altug Alkan, Jan 25 2016

A245241 Integers n such that 6 * 7^n + 1 is prime.

Original entry on oeis.org

0, 1, 4, 9, 99, 412, 2633, 5093, 5632, 28233, 36780, 47084, 53572
Offset: 1

Views

Author

Robert Price, Nov 14 2014

Keywords

Comments

All terms correspond to verified primes, that is, not merely probable primes.
a(14) > 2*10^5.

Examples

			4 is in this sequence because 6 * 7^4 + 1 = 14407, which is prime.

Crossrefs

Cf. A003307, A002235, A046865, A079906, A001771, A005541, A056725, A046867, A079907.
Cf. A005537, A005538, A005539, A216889, A216890, A247260.

Programs

  • Mathematica
    Select[Range[0,200000], PrimeQ[6 * 7^# + 1] &]

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)))

A326655 Numbers k such that 3*4^k+1 is prime.

Original entry on oeis.org

1, 3, 4, 6, 9, 15, 18, 33, 138, 204, 219, 267, 1104, 1408, 1584, 1956, 17175, 21147, 24075, 27396, 27591, 40095, 354984, 400989, 916248, 1145805, 2541153, 5414673
Offset: 1

Views

Author

Richard N. Smith, Jul 16 2019

Keywords

Comments

One half of the even terms in A002253.

Crossrefs

Numbers k such that r*(r+1)^k+1 is prime: A003306 (r=2), this sequence (r=3), A204322 (r=4), A247260 (r=5), A245241 (r=6), A269544 (r=7), A056799 (r=8), A056797 (r=9), A057462 (r=10), A251259 (r=11).
Showing 1-5 of 5 results.

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