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.

A247957 Numbers k such that 33^k + 2 is prime.

Original entry on oeis.org

0, 2, 26, 60, 218, 248, 399, 1175, 1244, 2670, 9300, 45216, 144412
Offset: 1

Views

Author

Vincenzo Librandi, Sep 28 2014

Keywords

Comments

Some terms correspond to probable primes. Lifchitz link shows that Ray Chandler discovered 9300, and Lelio R Paula found that 45216 is in the sequence. - Jens Kruse Andersen, Sep 29 2014
Terms in the similar sequence, 53^k+2, begin with 0, 7, 14483 with the next term > 2*10^5. - Robert Price, Mar 28 2015
Confirmed that 45216 is a(12). - Robert Price, Apr 14 2015
a(14) > 2*10^5. - Robert Price, Apr 14 2015

Links

Crossrefs

Cf. numbers n such that k^n+2 is prime: A051783 (k=3), A087885 (k=5), A090649 (k=9), A109076 (k=11), A138048 (k=15), A113480 (k=17), A138049 (k=21), A138050 (k=23), A138051 (k=27), A087886 (k=29), this sequence (k=33), A247958 (k=35), A247959 (k=39), A247960 (k=41), A247961 (k=45); (0, 113) for k=47; A247962 (k=51); A247963 (k=57), A113481 (k=59).

Programs

  • Magma
    [n: n in [0..350]| IsPrime( 33^n + 2 )];
  • Maple
    A247957:=n->`if`(isprime(33^n+2),n,NULL): seq(A247957(n), n=0..1000); # Wesley Ivan Hurt, Sep 28 2014
  • Mathematica
    Select[Range[0,1000], PrimeQ[33^# + 2] &]
  • PARI
    is(n)=ispseudoprime(33^n+2) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(8)-a(11) from Jens Kruse Andersen, Sep 29 2014
a(12)-a(13) from Robert Price, Apr 14 2015

A138048 Numbers k such that 15^k + 2 is prime.

Original entry on oeis.org

0, 1, 2, 4, 5, 10, 11, 16, 20, 52, 75, 106, 112, 132, 371, 3264, 3424, 5477, 7516, 10365, 44557, 150706
Offset: 1

Views

Author

Alexander Adamchuk, Mar 02 2008

Keywords

Comments

No further terms < 100000. - Ray Chandler, Aug 05 2011
a(23) > 2*10^5. - Robert Price, Jun 23 2015

Links

Crossrefs

Cf. A051783 (k such that 3^k + 2 is prime).
Cf. A087885 (k such that 5^k + 2 is prime).
Cf. A090649, A109076, A113480, A138049, A138050, A138051, A087886, A113481.

Programs

  • Mathematica
    Do[ f = 15^n + 2; If[ PrimeQ[ f ], Print[ {n, f} ] ], {n, 1, 371} ]
  • PARI
    is(n)=ispseudoprime(15^n+2) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(16)-a(19) from Ray Chandler, Jul 30 2011
a(20) found by Lelio R Paula, Dec 2006
a(21) from Ray Chandler, Jul 31 2011
a(22) from Robert Price, Jun 23 2015

A138049 Numbers k such that 21^k + 2 is prime.

Original entry on oeis.org

0, 1, 2, 4, 7, 24, 40, 112, 310, 1026, 1286, 36566, 43717, 53753
Offset: 1

Views

Author

Alexander Adamchuk, Mar 02 2008

Keywords

Comments

No further terms < 100000. - Ray Chandler, Aug 11 2011
a(15) > 2*10^5. - Robert Price, Jul 14 2015

Links

Crossrefs

Cf. A051783 (k such that 3^k + 2 is prime).
Cf. A087885 (k such that 5^k + 2 is prime).
Cf. A090649, A109076, A113480, A138048, A138050, A138051, A087886, A113481.

Programs

  • Mathematica
    Do[ f = 21^n + 2; If[ PrimeQ[ f ], Print[ {n, f} ] ], {n, 1, 310} ]
  • PARI
    is(n)=ispseudoprime(21^n+2) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

1026 from Herman Jamke (hermanjamke(AT)fastmail.fm), May 01 2008
1286 and 36566 from Ray Chandler, Jul 31 2011
43717 from Ray Chandler, Aug 01 2011
53753 from Ray Chandler, Aug 02 2011

A138050 Numbers k such that 23^k + 2 is prime.

Original entry on oeis.org

0, 11, 39, 323, 12415, 14655, 27679
Offset: 1

Views

Author

Alexander Adamchuk, Mar 02 2008

Keywords

Comments

No further terms < 100000. - Ray Chandler, Aug 03 2011

Links

Crossrefs

Cf. A051783 (k such that 3^k + 2 is prime).
Cf. A087885 (k such that 5^k + 2 is prime).
Cf. A090649, A109076, A113480, A138048, A138049, A138051, A087886, A113481.

Programs

  • Mathematica
    Do[ f = 23^n + 2; If[ PrimeQ[ f ], Print[ {n, f} ] ], {n, 1, 323} ]
  • PARI
    is(n)=ispseudoprime(23^n+2) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(5)-a(7) from Ray Chandler, Aug 01 2011

A138051 Numbers k such that 27^k + 2 is prime.

Original entry on oeis.org

0, 1, 5, 8, 12, 21, 41, 42, 81, 105, 121, 377, 501, 2401, 14597, 35381, 59476, 120536
Offset: 1

Views

Author

Alexander Adamchuk, Mar 02 2008

Keywords

Comments

All terms are the exact thirds of terms of A051783 that are divisible by 3.

Links

Crossrefs

Cf. A051783 (3^k + 2 is prime), A087885 (5^k + 2 is prime).
Cf. A090649, A109076, A113480, A138048, A138049, A138050, A087886, A113481.
Cf. A176495.

Programs

  • Mathematica
    Do[ f = 27^n + 2; If[ PrimeQ[ f ], Print[ {n, f} ] ], {n, 1, 2500} ]
  • PARI
    is(n)=ispseudoprime(27^n+2) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(15)-a(17) from A051783 by Ray Chandler, Aug 06 2011
a(18) from Robert Price, May 12 2019

A138066 Least k > 0 such that (2n-1)^k + 2 is prime, or 0 if no such number exists.

Original entry on oeis.org

1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 11, 0, 1, 1, 0, 2, 1, 0, 1, 1, 0, 1, 113, 0, 1, 7, 0, 1, 1, 0, 3, 1, 0, 1, 1, 0, 12, 1, 0, 1, 3, 0, 1, 255, 0, 8, 1, 0, 1, 1, 0, 1, 1, 0, 1, 3, 0, 2, 15, 0, 2, 1, 0, 1, 23, 0, 1, 1, 0, 4, 3, 0, 1, 1, 0, 3, 1, 0, 136, 1, 0, 1
Offset: 1

Views

Author

Alexander Adamchuk, Mar 02 2008

Keywords

Comments

a(3n+1) = 0 for n > 0.
a(84) > 100000. - Ray Chandler, Aug 10 2011

Crossrefs

Cf. A084713 (smallest prime of the form (2n-1)^k + 2, or 0 if no such number exists).
Cf. A138067 (least k > 1 such that (2n-1)^k + 2 is prime, or 0 if no such number exists).
Cf. A051783 (k such that 3^k + 2 is prime).
Cf. A087885 (k such that 5^k + 2 is prime).
Cf. A090649, A109076, A113480, A138048, A138049, A138050, A138051, A087886, A113481.

A138067 Least k > 1 such that (2n-1)^k + 2 is prime, or 0 if no such number exists.

Original entry on oeis.org

2, 2, 3, 0, 2, 5, 0, 2, 105, 0, 2, 11, 0, 5, 3, 0, 2, 15, 0, 2, 9, 0, 2, 113, 0, 5, 7, 0, 2, 27, 0, 3, 3, 0, 3, 3, 0, 12, 61, 0, 2, 3, 0, 4, 255, 0, 8, 63, 0, 2, 9, 0, 2, 3473, 0, 2, 3, 0, 2, 15, 0, 2, 87, 0, 3, 23, 0, 36, 1861, 0, 4, 3, 0, 2, 5, 0, 3, 7, 0, 136, 425, 0, 11
Offset: 1

Views

Author

Alexander Adamchuk, Mar 02 2008

Keywords

Comments

a(3n+1) = 0 for n > 0.
a(84) > 100000. - Ray Chandler, Aug 10 2011

Crossrefs

Cf. A084713 (smallest prime of the form (2n-1)^k + 2, or 0 if no such number exists).
Cf. A138066 (least k > 0 such that (2n-1)^k + 2 is prime, or 0 if no such number exists).
Cf. A051783 (k such that 3^k + 2 is prime).
Cf. A087885 (k such that 5^k + 2 is prime).
Cf. A090649, A109076, A113480, A138048, A138049, A138050, A138051, A087886, A113481.

Extensions

a(54)-a(83) from Donovan Johnson, Oct 29 2008

A248547 Numbers n such that 75^n+2 is prime.

Original entry on oeis.org

0, 12, 28, 53, 65, 504, 1967, 6915
Offset: 1

Views

Author

Vaclav Kotesovec, Oct 08 2014

Keywords

Comments

Dedicated to N. J. A. Sloane for his 75th birthday!
Next term, if it exists, is greater than 10000.
Next term, if it exists, is greater than 50000. - Michael S. Branicky, May 21 2025

Crossrefs

Cf. A051783, A087885, A090649, A109076, A138048, A113480, A138049, A138050.

Programs

  • Magma
    [n: n in [0..200] | IsPrime(75^n+2)]; // Vincenzo Librandi, Oct 08 2014
  • Mathematica
    Select[Range[0, 1000], PrimeQ[75^# + 2] &]
  • PARI
    is(n)=ispseudoprime(75^n+2) \\ Charles R Greathouse IV, Jun 13 2017
Showing 1-8 of 8 results.

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