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 122 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

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

A062572 Numbers k such that 6^k - 5^k is prime.

Original entry on oeis.org

2, 5, 11, 13, 23, 61, 83, 421, 1039, 1511, 31237, 60413, 113177, 135647, 258413
Offset: 1

Views

Author

Mike Oakes, May 18 2001, May 19 2001

Keywords

Comments

The 809- and 1176-digit numbers associated with the terms 1039 and 1511 have been certified prime with Primo. - Rick L. Shepherd, Nov 15 2002

Examples

			2 is in the sequence because 6^2 - 5^2 = 36 - 25 = 11, which is prime.
3 is not in the sequence because 6^3 - 5^3 = 216 - 125 = 91 = 7 * 13, which is not prime.
		

Crossrefs

Programs

  • Mathematica
    Select[Range[1000], PrimeQ[6^# - 5^#] &] (* Alonso del Arte, Sep 04 2013 *)
  • PARI
    forprime(p=2,1e4,if(ispseudoprime(6^n-5^n),print1(p", "))) \\ Charles R Greathouse IV, Jun 10 2011

Extensions

Edited by T. D. Noe, Oct 30 2008
Two more terms (31237 and 60413) found by Predrag Minovic in 2004 corresponding to probable primes with 24308 and 47011 digits. Jean-Louis Charton, Oct 06 2010
Two more terms (113177 and 135647) found by Jean-Louis Charton in 2009 corresponding to probable primes with 88069 and 105554 digits. Jean-Louis Charton, Oct 13 2010
a(15) from Jean-Louis Charton, Apr 08 2013

A062666 Numbers k such that 100^k - 99^k is prime.

Original entry on oeis.org

2, 5, 19, 59, 1013, 2371, 13967, 44683
Offset: 1

Views

Author

Mike Oakes, May 18 2001, May 19 2001

Keywords

Comments

Terms > 10000 correspond to probable primes.
a(9) > 10^5. - Robert Price, Jul 10 2013

Crossrefs

Programs

Extensions

Edited by T. D. Noe, Oct 30 2008
a(7)-a(8) from Robert Price, Jul 10 2013

A062589 Numbers k such that 23^k - 22^k is prime, or a strong pseudoprime.

Original entry on oeis.org

229, 241, 673, 5387, 47581
Offset: 1

Views

Author

Mike Oakes, May 18 2001, May 19 2001

Keywords

Comments

Terms greater than 1000 often correspond to "unproven" strong pseudoprimes.
a(6) > 10^5. - Robert Price, Aug 22 2012

Crossrefs

Extensions

a(5) from Robert Price, Aug 22 2012
Edited by M. F. Hasler, Sep 21 2013

A062587 Numbers k such that 21^k - 20^k is prime.

Original entry on oeis.org

2, 19, 41, 43, 337, 479, 9127, 37549, 44017, 59971, 128327, 176191, 193601
Offset: 1

Views

Author

Mike Oakes, May 18 2001, May 19 2001

Keywords

Comments

Terms greater than 1000 may correspond to (unproven) strong pseudoprimes.

Crossrefs

Programs

Extensions

a(8) from Jean-Louis Charton, Feb 29 2012
a(9) and a(10) from Robert Price, May 30 2012
Edited by M. F. Hasler, Sep 16 2013
a(11) added by Jean-Louis Charton, Nov 24 2014
a(12) added by Jean-Louis Charton, Feb 05 2015
a(13) added by Jean-Louis Charton, Feb 18 2015

A128027 Numbers n such that (11^n - 3^n)/8 is prime.

Original entry on oeis.org

3, 5, 19, 31, 367, 389, 431, 2179, 10667, 13103, 90397
Offset: 1

Views

Author

Alexander Adamchuk, Feb 11 2007

Keywords

Comments

All terms are primes.
No other terms < 10^5.

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, A128028, A128029, A128030, A128031, A128032.

Programs

  • Magma
    [p: p in PrimesUpTo(400) | IsPrime((11^p-3^p) div 8)]; // Vincenzo Librandi, Nov 20 2014
    
  • Maple
    A128027:=n->`if`(isprime((11^n-3^n)/8),n,NULL): seq(A128027(n),n=1..1000); # Wesley Ivan Hurt, Nov 19 2014
  • Mathematica
    k=8; Select[ Prime[ Range[1,200] ], PrimeQ[ ((k+3)^# - 3^#)/k ]& ]
    Do[If[PrimeQ[(11^n - 3^n)/8], Print[n]], {n, 10^4}] (* Ryan Propper, Mar 17 2007 *)
    Select[Prime[Range[1200]], PrimeQ[(11^# - 3^#)/8] &] (* Vincenzo Librandi, Nov 20 2014 *)
  • PARI
    is(n)=ispseudoprime((11^n - 3^n)/8) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(8) from Ryan Propper, Mar 17 2007
a(9) from Farideh Firoozbakht, Apr 04 2007
a(10)=13103, a(11)=90397 from Robert Price, Apr 24 2011

A128024 Numbers k such that (7^k - 3^k)/4 is prime.

Original entry on oeis.org

3, 7, 19, 109, 131, 607, 863, 2917, 5923, 12421, 187507, 353501, 817519
Offset: 1

Views

Author

Alexander Adamchuk, Feb 11 2007

Keywords

Comments

All terms are primes. No other terms < 1000000.

Crossrefs

Programs

  • Mathematica
    k=4; Select[ Prime[ Range[1,200] ], PrimeQ[ ((k+3)^# - 3^#)/k ]& ]
  • PARI
    forprime(p=3,1e5,if(ispseudoprime((7^p-3^p)/4),print1(p", "))) \\ Charles R Greathouse IV, Jun 01 2011
    
  • Python
    from sympy import isprime
    def aupto(lim): return [k for k in range(lim+1) if isprime((7**k-3**k)//4)]
    print(aupto(900)) # Michael S. Branicky, Mar 07 2021

Extensions

a(8)-a(9) from Farideh Firoozbakht, Apr 08 2007
a(10) from Robert Price, Jun 01 2011
a(11)-a(13) from Jon Grantham, Jul 29 2023

A128026 Numbers n such that (10^n - 3^n)/7 is prime.

Original entry on oeis.org

2, 3, 5, 37, 599, 38393, 51431, 118681, 376417
Offset: 1

Views

Author

Alexander Adamchuk, Feb 11 2007

Keywords

Comments

All terms are primes.
No other terms < 1000000.

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.

Programs

  • Mathematica
    k=7; Select[ Prime[ Range[1,200] ], PrimeQ[ ((k+3)^# - 3^#)/k ]& ]
  • PARI
    forprime(p=2,1e4,if(ispseudoprime((10^p-3^p)/7),print1(p", "))) \\ Charles R Greathouse IV, Jun 05 2011

Extensions

a(6)-a(7) from Robert Price, Jun 04 2011
a(8)-a(9) from Jon Grantham, Jul 29 2023

A128028 Numbers k such that (13^k - 3^k)/10 is prime.

Original entry on oeis.org

7, 31, 41, 269, 283, 7333, 8803
Offset: 1

Views

Author

Alexander Adamchuk, Feb 11 2007

Keywords

Comments

All terms are primes.
No other terms exist < 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, A128029, A128030, A128031, A128032.

Programs

  • Mathematica
    k=10; Select[ Prime[ Range[1,200] ], PrimeQ[ ((k+3)^# - 3^#)/k ]& ]
  • PARI
    is(n)=isprime((13^n-3^n)/10) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

One more term from Farideh Firoozbakht, Apr 03 2007
a(7)=8803 from Robert Price, Aug 12 2011

A128025 Numbers k such that (8^k - 3^k)/5 is prime.

Original entry on oeis.org

2, 3, 7, 19, 31, 67, 89, 9227, 43891, 854149
Offset: 1

Views

Author

Alexander Adamchuk, Feb 11 2007

Keywords

Comments

All terms are primes.
Verified the first 8 terms in sequence. Also, the next number in the sequence, if one exists is > 43691. - Robert Price, Mar 16 2010
a(10) > 10^5. - Robert Price, Jul 27 2011
a(11) > 10^6. - Jon Grantham, Jul 29 2023

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, A128026, A128027, A128028, A128029, A128030, A128031, A128032.

Programs

  • Mathematica
    k=5; Select[ Prime[ Range[1,200] ], PrimeQ[ ((k+3)^# - 3^#)/k ]& ]
  • PARI
    is(n)=isprime((8^n-3^n)/5) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

9227 from Farideh Firoozbakht, Apr 08 2007
a(9) from Robert Price, Jul 27 2011
a(10) from Jon Grantham, Jul 29 2023
Showing 1-10 of 122 results. Next