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 1-10 of 31 results. Next

A059802 Numbers k such that 5^k - 4^k is prime.

Original entry on oeis.org

3, 43, 59, 191, 223, 349, 563, 709, 743, 1663, 5471, 17707, 19609, 35449, 36697, 45259, 91493, 246497, 265007, 289937
Offset: 1

Views

Author

Mike Oakes, Feb 23 2001

Keywords

Comments

Some of the larger terms may only correspond to probable primes.
5^1663 - 4^1663, a 1163-digit number, has been certified prime with Primo. - Rick L. Shepherd, Nov 13 2002
4 more terms found by Predrag Minovic in 2004: 35449, 36697, 45259, 91493. Corresponding numbers of decimal digits are 24778, 25651, 31635, 63951. - Alexander Adamchuk, Dec 02 2006

Crossrefs

Cf. A005060.
Cf. A000043, A057468, A059801, A128335, etc.

Programs

  • Mathematica
    Select[Range[1000], PrimeQ[5^# - 4^#] &] (* Alonso del Arte, Sep 09 2013 *)
  • PARI
    forprime(p=2,1e5,if(ispseudoprime(5^p-4^p),print1(p", "))) \\ Charles R Greathouse IV, Jun 10 2011

Extensions

New term 246497 found by Jean-Louis Charton in 2008 corresponding to a probable prime with 172295 digits - Jean-Louis Charton, Sep 02 2009
New term a(19) = 265007 found by Jean-Louis Charton, Feb 19 2013
a(20) = 289937 found by Jean-Louis Charton, Mar 15 2013

A128344 Numbers k such that (7^k - 5^k)/2 is prime.

Original entry on oeis.org

3, 5, 7, 113, 397, 577, 7573, 14561, 58543, 100019, 123407, 136559, 208283, 210761, 457871, 608347, 636043
Offset: 1

Views

Author

Alexander Adamchuk, Feb 27 2007

Keywords

Comments

All terms are primes.
No other terms less than 10^5. - Robert Price, May 28 2012
No other terms less than 10^6. - Jon Grantham, Jul 29 2023

Links

Crossrefs

Cf. A062572, A128345, A128346, A128347, A128348, A128349, A128350, A128351, A128352, A128353, A128354. Cf. A004061, A082182, A121877, A059802. Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128338, A128339, A128340, A128341, A128342.

Programs

  • Mathematica
    k=7; Do[p=Prime[n]; f=(k^p-5^p)/(k-5); If[ PrimeQ[f], Print[p] ], {n,1,100}]
  • PARI
    is(n)=isprime((7^n-5^n)/2) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(7)-a(9) from Robert Price, May 28 2012
a(10)-a(17) from Jon Grantham, Jul 29 2023

A128336 Numbers k such that (6^k + 5^k)/11 is prime.

Original entry on oeis.org

3, 5, 17, 397, 409, 643, 1783, 2617, 4583, 8783
Offset: 1

Views

Author

Alexander Adamchuk, Feb 27 2007

Keywords

Comments

All terms are primes.
No other terms less than 100000. - Robert Price, May 11 2012

Crossrefs

Cf. A057171, A082387, A122853, A128335, A128337, A128338, A128339, A128340, A128341, A128342, A128343, A004061, A082182, A121877, A059802, A062572, A128344, A128345, A128346, A128347, A128348, A128349, A128350, A128351, A128352, A128353, A128354.

Programs

  • Mathematica
    k=6; Do[p=Prime[n]; f=(k^p+5^p)/(k+5); If[ PrimeQ[f], Print[p] ], {n,1,100}]
  • PARI
    forprime(p=3,1e4,if(ispseudoprime((6^p+5^p)/11),print1(p", "))) \\ Charles R Greathouse IV, Jul 16 2011

Extensions

a(7)-a(9) from Alexander Adamchuk, May 04 2010
One more term (8783) added (unknown discoverer) corresponding to a probable prime with 6834 digits by Jean-Louis Charton, Oct 06 2010

A128347 Numbers k such that (11^k - 5^k)/6 is prime.

Original entry on oeis.org

5, 41, 149, 229, 263, 739, 3457, 20269, 98221
Offset: 1

Views

Author

Alexander Adamchuk, Feb 27 2007

Keywords

Comments

All terms are primes.
a(10) > 10^5. - Robert Price, Jan 24 2013

Crossrefs

Cf. A062572, A128344, A128345, A128346, A128348, A128349, A128350, A128351, A128352, A128353, A128354. Cf. A004061, A082182, A121877, A059802. Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128338, A128339, A128340, A128341, A128342.

Programs

  • Mathematica
    k=11; Do[p=Prime[n]; f=(k^p-5^p)/(k-5); If[ PrimeQ[f], Print[p] ], {n,1,100}]
  • PARI
    is(n)=isprime((11^n-5^n)/6) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(7)-a(9) from Robert Price, Jan 24 2013

A128342 Numbers k such that (13^k + 5^k)/18 is prime.

Original entry on oeis.org

13, 19, 31, 359, 487, 757, 761, 1667, 2551, 3167, 6829
Offset: 1

Views

Author

Alexander Adamchuk, Feb 27 2007

Keywords

Comments

All terms are primes.
No other terms below 23600. - Max Alekseyev, Feb 01 2010
a(12) > 10^5. - Robert Price, Apr 30 2013

Crossrefs

Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128338, A128339, A128340, A128341, A128343. Cf. A004061, A082182, A121877, A059802. Cf. A062572, A128344, A128345, A128346, A128347, A128348, A128349, A128350, A128351, A128352, A128353, A128354.

Programs

  • Mathematica
    k=13; Do[p=Prime[n]; f=(k^p+5^p)/(k+5); If[ PrimeQ[f], Print[p] ], {n,1,100}]
  • PARI
    is(n)=isprime((13^n+5^n)/18) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

Four more terms from Max Alekseyev, Feb 01 2010

A128341 Numbers k such that (12^k + 5^k)/17 is prime.

Original entry on oeis.org

3, 5, 13, 347, 977, 1091, 4861, 4967, 34679
Offset: 1

Views

Author

Alexander Adamchuk, Feb 27 2007

Keywords

Comments

All terms are primes.
a(10) > 10^5. - Robert Price, May 05 2013

Crossrefs

Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128338, A128339, A128340, A128342, A128343.
Cf. A004061, A082182, A121877, A059802.
Cf. A062572, A128344, A128345, A128346, A128347, A128348, A128349, A128350, A128351, A128352, A128353, A128354.

Programs

  • Mathematica
    k=12; Do[p=Prime[n]; f=(k^p+5^p)/(k+5); If[ PrimeQ[f], Print[p] ], {n,1,100}]
Select[Range[1100],PrimeQ[(12^#+5^#)/17]&] (* Harvey P. Dale, Jul 24 2012 *)
  • PARI
    is(n)=isprime((12^n+5^n)/17) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

Two more terms (a(7) and a(8)) from Harvey P. Dale, Jul 24 2012
a(9) from Robert Price, May 05 2013

A128339 Numbers k such that (9^k + 5^k)/14 is prime.

Original entry on oeis.org

3, 5, 13, 17, 43, 127, 229, 277, 6043, 11131, 11821
Offset: 1

Views

Author

Alexander Adamchuk, Feb 27 2007

Keywords

Comments

All terms are primes.
a(12) > 10^5. - Robert Price, Dec 26 2012

Crossrefs

Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128338, A128340, A128341, A128342, A128343. Cf. A004061, A082182, A121877, A059802. Cf. A062572, A128344, A128345, A128346, A128347, A128348, A128349, A128350, A128351, A128352, A128353, A128354.

Programs

  • Magma
    [n: n in [3..300] |IsPrime((9^n + 5^n) div 14)]; // Vincenzo Librandi, Nov 02 2018
  • Mathematica
    k=9; Do[p=Prime[n]; f=(k^p+5^p)/(k+5); If[ PrimeQ[f], Print[p] ], {n,1,100}]
  • PARI
    is(n)=isprime((9^n+5^n)/14) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

3 more PRP terms from Sean A. Irvine, Oct 01 2009

A128340 Numbers k such that (11^k + 5^k)/16 is prime.

Original entry on oeis.org

7, 11, 181, 421, 2297, 2797, 4129, 4139, 7151, 29033
Offset: 1

Views

Author

Alexander Adamchuk, Feb 27 2007

Keywords

Comments

All terms are primes.
a(11) > 10^5. - Robert Price, Feb 09 2013

Crossrefs

Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128338, A128339, A128341, A128342, A128343.
Cf. A004061, A082182, A121877, A059802.
Cf. A062572, A128344, A128345, A128346, A128347, A128348, A128349, A128350, A128351, A128352, A128353, A128354.

Programs

  • Mathematica
    k=11; Do[p=Prime[n]; f=(k^p+5^p)/(k+5); If[ PrimeQ[f], Print[p] ], {n,1,100}]
  • PARI
    is(n)=isprime((11^n+5^n)/16) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(5)-a(10) from Robert Price, Feb 09 2013

A128346 Numbers k such that (9^k - 5^k)/4 is prime.

Original entry on oeis.org

3, 11, 17, 173, 839, 971, 40867, 45821, 147503
Offset: 1

Views

Author

Alexander Adamchuk, Feb 27 2007

Keywords

Comments

All terms are primes.
a(9) > 10^5. - Robert Price, Jan 19 2013
a(10) > 10^6. - Jon Grantham, Jul 29 2023

Links

Crossrefs

Cf. A062572, A128344, A128345, A128347, A128348, A128349, A128350, A128351, A128352, A128353, A128354.
Cf. A004061, A082182, A121877, A059802.
Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128338, A128339, A128340, A128341, A128342.

Programs

  • Mathematica
    k=9; Do[p=Prime[n]; f=(k^p-5^p)/(k-5); If[ PrimeQ[f], Print[p] ], {n,1,100}]
  • PARI
    is(n)=isprime((9^n-5^n)/4) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(7)-a(8) from Robert Price, Jan 19 2013
a(8) corrected by Robert Price, Jan 20 2013
a(9) from Jon Grantham, Jul 29 2023

A128348 Numbers k such that (12^k - 5^k)/7 is prime.

Original entry on oeis.org

2, 3, 31, 41, 53, 101, 421, 1259, 4721, 45259
Offset: 1

Views

Author

Alexander Adamchuk, Feb 27 2007

Keywords

Comments

All terms are primes.
Primality of the primes formed by a(8) and a(9) were certified by Primo. - Ray G. Opao, Jul 01 2012
a(11) > 10^5. - Robert Price, Mar 02 2013

Crossrefs

Cf. A062572, A128344, A128345, A128346, A128347, A128349, A128350, A128351, A128352, A128353, A128354.
Cf. A004061, A082182, A121877, A059802.
Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128338, A128339, A128340, A128341, A128342.

Programs

  • Mathematica
    k=12; Do[p=Prime[n]; f=(k^p-5^p)/(k-5); If[ PrimeQ[f], Print[p] ], {n,1,100}]
  • PARI
    is(n)=isprime((12^n-5^n)/7) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(8) and a(9) from Ray G. Opao, Jul 01 2012
a(10) from Robert Price, Mar 02 2013
Showing 1-10 of 31 results. Next

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