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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A128075 Numbers k such that (3^k + 19^k)/22 is prime.

Original entry on oeis.org

3, 61, 71, 109, 9497, 36007, 50461, 66919
Offset: 1

Views

Author

Alexander Adamchuk, Feb 14 2007

Keywords

Comments

All terms are primes.
a(9) > 10^5. - Robert Price, Jul 21 2013

Crossrefs

Cf. A007658 (numbers k such that (3^k + 1)/4 is prime).
Cf. A057469 (numbers k such that (3^k + 2^k)/5 is prime).
Cf. A122853 (numbers k such that (3^k + 5^k)/8 is prime).
Cf. A128066, A128067, A128068, A128069, A128070, A128071, A128072, A128073, A128074.
Cf. A059801 (numbers k such that 4^k - 3^k is prime).
Cf. A121877 (numbers k such that (5^k - 3^k)/2 is prime).
Cf. A128024, A128025, A128026, A128027, A128028, A128029, A128030, A128031, A128032.

Programs

  • Mathematica
    k=19; Do[ p=Prime[n]; f=(3^p+k^p)/(k+3); If[ PrimeQ[f], Print[p]], {n,1,9592} ]
  • PARI
    is(n)=isprime((3^n+19^n)/22) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(5)-a(8) from Robert Price, Jul 21 2013

A128343 Numbers k such that (14^k + 5^k)/19 is prime.

Original entry on oeis.org

3, 7, 17, 79, 17477, 19319, 49549
Offset: 1

Views

Author

Alexander Adamchuk, Feb 27 2007

Keywords

Comments

All terms are primes.
a(8) > 10^5. - Robert Price, May 20 2013

Crossrefs

Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128338, A128339, A128340, A128341, A128342.
Cf. A004061, A082182, A121877, A059802.
Cf. A062572, A128344, A128345, A128346, A128347, A128348, A128349, A128350, A128351, A128352, A128353, A128354.

Programs

  • Mathematica
    k=14; Do[p=Prime[n]; f=(k^p+5^p)/(k+5); If[ PrimeQ[f], Print[p] ], {n,1,100}]
  • PARI
    is(n)=isprime((14^n+5^n)/19) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(5)-a(7) from Robert Price, May 20 2013

A128072 Numbers k such that (3^k + 14^k)/17 is prime.

Original entry on oeis.org

3, 7, 71, 251, 1429, 2131, 2689, 36683, 60763
Offset: 1

Views

Author

Alexander Adamchuk, Feb 14 2007

Keywords

Comments

All terms are primes.
a(10) > 10^5. - Robert Price, Apr 20 2013

Crossrefs

Cf. A007658 (numbers k such that (3^k + 1)/4 is prime).
Cf. A057469 (numbers k such that (3^k + 2^k)/5 is prime).
Cf. A122853 (numbers k such that (3^k + 5^k)/8 is prime).
Cf. A128066, A128067, A128068, A128069, A128070, A128071, A128073, A128074, A128075.
Cf. A059801 (numbers k such that 4^k - 3^k is prime).
Cf. A121877 (numbers k such that (5^k - 3^k)/2 is prime).
Cf. A128024, A128025, A128026, A128027, A128028, A128029, A128030, A128031, A128032.

Programs

  • Mathematica
    k=14; Do[ p=Prime[n]; f=(3^p+k^p)/(k+3); If[ PrimeQ[f], Print[p]], {n,1,100} ]
  • PARI
    is(n)=isprime((3^n+14^n)/17) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

3 more terms from Ryan Propper, Jan 28 2008
a(8)-a(9) from Robert Price, Apr 20 2013

A128073 Numbers k such that (3^k + 16^k)/19 is prime.

Original entry on oeis.org

5, 17, 61, 673, 919, 2089, 86939
Offset: 1

Views

Author

Alexander Adamchuk, Feb 14 2007

Keywords

Comments

All terms are primes.
a(8) > 10^5 - Robert Price, Jun 29 2013

Crossrefs

Cf. A007658 (numbers k such that (3^k + 1)/4 is prime).
Cf. A057469 (numbers k such that (3^k + 2^k)/5 is prime).
Cf. A122853 (numbers k such that (3^k + 5^k)/8 is prime).
Cf. A128066, A128067, A128068, A128069, A128070, A128071, A128072, A128074, A128075.
Cf. A059801 (numbers k such that 4^k - 3^k is prime).
Cf. A121877 (numbers k such that (5^k - 3^k)/2 is prime).
Cf. A128024, A128025, A128026, A128027, A128028, A128029, A128030, A128031, A128032.

Programs

  • Mathematica
    k=16; Do[ p=Prime[n]; f=(3^p+k^p)/(k+3); If[ PrimeQ[f], Print[p]], {n,1,100} ]
  • PARI
    is(n)=isprime((3^n+16^n)/19) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(5) from Alexander Adamchuk, Feb 14 2007
a(6) and a(7) from Robert Price, Jun 29 2013

A128067 Numbers k such that (3^k + 7^k)/10 is prime.

Original entry on oeis.org

3, 13, 31, 313, 3709, 7933, 14797, 30689, 38333
Offset: 1

Views

Author

Alexander Adamchuk, Feb 14 2007

Keywords

Comments

All terms are primes.
a(10) > 10^5. - Robert Price, Oct 03 2012

Crossrefs

Cf. A007658 = numbers n such that (3^n + 1)/4 is prime. Cf. A057469 = numbers n such that (3^n + 2^n)/5 is prime. Cf. A122853 = numbers n such that (3^n + 5^n)/8 is prime. Cf. A128066, A128068, A128069, A128070, A128071, A128072, A128073, A128074, A128075. 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, A128031, A128032.

Programs

  • Mathematica
    k=7; Do[ p=Prime[n]; f=(3^p+k^p)/(k+3); If[ PrimeQ[f], Print[p]], {n,1,100} ]
  • PARI
    is(n)=isprime((3^n+7^n)/10) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

More terms from Ryan Propper, Apr 02 2007
a(7)-a(9) from Robert Price, Oct 03 2012

A128069 Numbers k such that (3^k + 10^k)/13 is prime.

Original entry on oeis.org

3, 19, 31, 101, 139, 167, 1097, 43151, 60703, 90499
Offset: 1

Views

Author

Alexander Adamchuk, Feb 14 2007

Keywords

Comments

All terms are primes.
Next term is greater than 6700. - Stefan Steinerberger, May 11 2007
a(11) > 10^5. - Robert Price, Jan 15 2013

Crossrefs

Cf. A007658 = numbers n such that (3^n + 1)/4 is prime. Cf. A057469 = numbers n such that (3^n + 2^n)/5 is prime. Cf. A122853 = numbers n such that (3^n + 5^n)/8 is prime. Cf. A128066, A128067, A128068, A128070, A128071, A128072, A128073, A128074, A128075. 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, A128031, A128032.

Programs

  • Mathematica
    k=10; Do[ p=Prime[n]; f=(3^p+k^p)/(k+3); If[ PrimeQ[f], Print[p]], {n,1,100} ]
  • PARI
    is(n)=isprime((3^n+10^n)/13) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(7) from Alexander Adamchuk, Feb 14 2007
a(8)-a(10) from Robert Price, Jan 15 2013

A128070 Numbers k such that (3^k + 11^k)/14 is prime.

Original entry on oeis.org

3, 103, 271, 523, 23087, 69833
Offset: 1

Views

Author

Alexander Adamchuk, Feb 14 2007

Keywords

Comments

All terms are primes.
a(7) > 10^5. - Robert Price, Mar 04 2013

Crossrefs

Cf. A007658 (numbers k such that (3^k + 1)/4 is prime).
Cf. A057469 (numbers k such that (3^k + 2^k)/5 is prime).
Cf. A122853 (numbers k such that (3^k + 5^k)/8 is prime).
Cf. A128066, A128067, A128068, A128069, A128071, A128072, A128073, A128074, A128075.
Cf. A059801 (numbers k such that 4^k - 3^k is prime).
Cf. A121877 (numbers k such that (5^k - 3^k)/2 is prime).
Cf. A128024, A128025, A128026, A128027, A128028, A128029, A128030, A128031, A128032.

Programs

  • Mathematica
    k=11; Do[ p=Prime[n]; f=(3^p+k^p)/(k+3); If[ PrimeQ[f], Print[p]], {n,1,100} ]
  • PARI
    is(n)=isprime((3^n+11^n)/14) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(5)-a(6) from Robert Price, Mar 04 2013

A128068 Numbers k such that (3^k + 8^k)/11 is prime.

Original entry on oeis.org

5, 163, 191, 229, 271, 733, 21059, 25237
Offset: 1

Views

Author

Alexander Adamchuk, Feb 14 2007

Keywords

Comments

All terms are primes.
a(9) > 10^5. - Robert Price, Mar 06 2013

Crossrefs

Cf. A007658 = numbers n such that (3^n + 1)/4 is prime. Cf. A057469 = numbers n such that (3^n + 2^n)/5 is prime. Cf. A122853 = numbers n such that (3^n + 5^n)/8 is prime. Cf. A128066, A128067, A128069, A128070, A128071, A128072, A128073, A128074, A128075. 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, A128031, A128032.

Programs

  • Mathematica
    k=8; Do[ p=Prime[n]; f=(3^p+k^p)/(k+3); If[ PrimeQ[f], Print[p]], {n,1,100} ]
  • PARI
    is(n)=isprime((3^n+8^n)/11) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(6) from Alexander Adamchuk, Feb 14 2007
a(7)-a(8) from Robert Price, Mar 06 2013

A121938 Primes of the form (3^k + 5^k)/2^3 = A074606(k)/8.

Original entry on oeis.org

19, 421, 10039, 95383574161, 2384331073699, 1925929944387235853055979210606894889560480247048440342330377620014353281101
Offset: 1

Views

Author

Zak Seidov, Sep 10 2006

Keywords

Comments

Corresponding numbers k such that (3^k + 5^k)/8 is prime are listed in A122853. All these numbers are primes. - Alexander Adamchuk, Sep 14 2006
The next term is too large to include. - Alexander Adamchuk, Sep 14 2006

Crossrefs

Cf. A074706, A122853, A081186, A079773, A121824, A121877, A005058, A005059, A121938, A109347.

Programs

  • Mathematica
    Do[f=5^n+3^n;If[PrimeQ[f/2^3],Print[{n,f/2^3}]],{n,1,1231}] (* Alexander Adamchuk, Sep 14 2006 *)

Formula

a(n) = (A122853(n)^3 + A122853(n)^5)/8. a(n) = A074606[A122853(n)]/8 = A081186[A122853(n)]/4. a(n) = A079773[A122853(n)]. - Alexander Adamchuk, Sep 14 2006

Extensions

More terms from Alexander Adamchuk, Sep 14 2006

A227979 Integers not of the form (a^k+b^k)/(a+b) for any positive integer values of a, b, k with b > a.

Original entry on oeis.org

2, 4, 6, 8, 9, 14, 16, 18, 22, 23, 24, 32, 33, 36, 38, 42, 44, 46, 47, 54, 56, 59, 62, 64, 66, 69, 71, 72, 77, 81, 83, 86, 88, 92, 94, 96, 98, 99, 107, 114, 118, 121, 126, 128, 131, 132, 134, 138, 141, 142, 144, 152, 154, 158, 161, 162, 166, 167, 168, 177
Offset: 1

Views

Author

Robert Price, Sep 30 2013

Keywords

Comments

This form, (a^k+b^k)/(a+b), is a generalization of the Fermat numbers.
Not all integers are in this set.
See A229791 for the complement of this sequence.

Links

Crossrefs

A few of the sequences using this form that identify primes are A000978, A007658, A057469, A128066, A057171, A082387, A122853, A128335.

Programs

  • Mathematica
    limit=200; lst = {}; Do[p = (a^k + b^k)/(a + b); If[p <= limit && IntegerQ[p], AppendTo[lst, p]], {k, Log[2,3*limit+1]}, {b, 2, limit*2}, {a, b-1}]; Complement[Range[limit], Union[lst]]
Previous Showing 21-30 of 31 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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