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.

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A128029 Numbers n such that (14^n - 3^n)/11 is prime.

Original entry on oeis.org

2, 5, 13, 67, 2657, 3547, 15649
Offset: 1

Views

Author

Alexander Adamchuk, Feb 11 2007

Keywords

Comments

All terms are primes.
There is no further term up to prime(1400)=11657. - Farideh Firoozbakht, Apr 04 2007
No other terms < 100,000.

Crossrefs

Cf. A028491 = numbers n such that (3^n - 1)/2 is prime. Cf. A057468 = numbers n such that 3^n - 2^n is prime. Cf. A059801 = numbers n such that 4^n - 3^n is prime. Cf. A121877 = numbers n such that (5^n - 3^n)/2 is a prime. Cf. A128024, A128025, A128026, A128027, A128028, A128030, A128031, A128032.

Programs

  • Mathematica
    k=11; Select[ Prime[ Range[1,200] ], PrimeQ[ ((k+3)^# - 3^#)/k ]& ]
  • PARI
    is(n)=isprime((14^n-3^n)/11) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

More terms from Farideh Firoozbakht, Apr 04 2007
Added term a(7)=15649 by Robert Price, Sep 12 2011

A128030 Numbers k such that (16^k - 3^k)/13 is prime.

Original entry on oeis.org

2, 3, 31, 467, 1747, 29683
Offset: 1

Views

Author

Alexander Adamchuk, Feb 11 2007

Keywords

Comments

All terms are primes.
No other terms < 100000.

Crossrefs

Cf. A028491 = numbers n such that (3^n - 1)/2 is prime. Cf. A057468 = numbers n such that 3^n - 2^n is prime. Cf. A059801 = numbers n such that 4^n - 3^n is prime. Cf. A121877 = numbers n such that (5^n - 3^n)/2 is a prime. Cf. A128024, A128025, A128026, A128027, A128028, A128029, A128031, A128032.

Programs

  • Mathematica
    k=13; Select[ Prime[ Range[1,200] ], PrimeQ[ ((k+3)^# - 3^#)/k ]& ]
  • PARI
    is(n)=isprime((16^n-3^n)/13) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

1747 from Farideh Firoozbakht, Apr 08 2007
a(6)=29683 from Robert Price, Sep 13 2011

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
Previous Showing 11-20 of 53 results. Next

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