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 53 results. Next

A123705 Primes of the form (5^p-3^p)/2, where prime p = Prime[A123704[n]] = A121877[n].

Original entry on oeis.org

609554401, 9536162033329, 5960417405949649, 2328306127701998147089, 355271367866755685756083382145169, 29387358770557187699218413428591111182510208390715375894150039546014062887655539136439569
Offset: 1

Views

Author

Alexander Adamchuk, Oct 08 2006

Keywords

Comments

Corresponding primes p are listed in A121877[n] = Prime[A123704[n]] = {13, 19, 23, 31, 47, 127, 223, 281, 2083, ...} Numbers n such that (5^n-3^n)/2 is a prime. Numbers n such that (5^p-3^p)/2 is prime, where p = Prime[n], are listed in A123704[n] = {6, 8, 9, 11, 15, 31, 48, 60, 314, ...}.

Crossrefs

Cf. A123704, A121877.

Programs

  • Mathematica
    Select[(5^#-3^#)/2&/@Prime[Range[50]],PrimeQ] (* Harvey P. Dale, Mar 30 2012 *)

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

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

A122853 Numbers k such that (3^k + 5^k)/8 = A074606(k)/8 is a prime.

Original entry on oeis.org

3, 5, 7, 17, 19, 109, 509, 661, 709, 1231, 12889, 13043, 26723, 43963, 44789
Offset: 1

Views

Author

Alexander Adamchuk, Sep 14 2006

Keywords

Comments

(3^k + 5^k)/8 = A074606(k)/8 = A081186(k)/4.
Corresponding primes of the form (3^k + 5^k)/2^3 are listed in {A121938(n)} = {A079773(a(n))} = {19, 421, 10039, 95383574161, 2384331073699, ...}.
No other terms less than 100000. - Robert Price, Apr 28 2012

Crossrefs

Cf. A074606, A081186, A121824, A121877, A005058, A005059, A121938, A109347, A079773.

Programs

  • Mathematica
    Do[f=5^n+3^n;If[PrimeQ[f/2^3],Print[{n,f/2^3}]],{n,1,1231}]
  • PARI
    select(n->isprime((3^n + 5^n)/8), vector(2000,i,i)) \\ Charles R Greathouse IV, Feb 13 2011

Extensions

a(11)-a(15) from Robert Price, Apr 28 2012

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.

Links

Crossrefs

Cf. A028491, A057468, A059801, A121877.
Cf. A128025, A128026, A128027, A128028, A128029, A128030, A128031, A128032.

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.

Links

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

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

Links

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

A128031 Numbers k such that (17^k - 3^k)/14 is prime.

Original entry on oeis.org

3, 11, 17, 491, 23029
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, A128030, A128032.

Programs

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

Extensions

a(5)=23029 from Robert Price, Nov 03 2011

A128032 Numbers k such that (19^k - 3^k)/16 is prime.

Original entry on oeis.org

73, 271, 421, 2711
Offset: 1

Views

Author

Alexander Adamchuk, Feb 11 2007

Keywords

Comments

All terms are primes.
No other terms <= 10^5. - Robert Price, Aug 27 2011

Crossrefs

Cf. A028491, A057468, A059801, A121877, A128024, A128025, A128026, A128027, A128028, A128029, A128030, A128031.

Programs

  • Mathematica
    k=16; Select[ Prime[ Range[1,200] ], PrimeQ[ ((k+3)^# - 3^#)/k ]& ]
  • PARI
    is(n)=isprime((19^n-3^n)/16) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

2711 from Farideh Firoozbakht, Apr 07 2007
Showing 1-10 of 53 results. Next

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