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 10 results.

A128066 Numbers k such that (3^k + 4^k)/7 is prime.

Original entry on oeis.org

3, 5, 19, 37, 173, 211, 227, 619, 977, 1237, 2437, 5741, 13463, 23929, 81223, 121271
Offset: 1

Views

Author

Alexander Adamchuk, Feb 14 2007

Keywords

Comments

All terms are primes.

Links

Crossrefs

Cf. A007658 = n such that (3^n + 1)/4 is prime; A057469 ((3^n + 2^n)/5); A122853 ((3^n + 5^n)/8).
Cf. A128067, A128068, A128069, A128070, A128071, A128072, A128073, A128074, A128075.
Cf. A059801 (4^n - 3^n); A121877 ((5^n - 3^n)/2).
Cf. A128024, A128025, A128026, A128027, A128028, A128029, A128030, A128031, A128032.

Programs

  • Maple
    a:=proc(n) if type((3^n+4^n)/7,integer)=true and isprime((3^n+4^n)/7)=true then n else fi end: seq(a(n),n=1..1500); # Emeric Deutsch, Feb 17 2007
  • Mathematica
    Do[ p=Prime[n]; f=(3^p+4^p)/(4+3); If[ PrimeQ[f], Print[p]], {n,1,100} ]
  • PARI
    f(n)=(3^n + 4^n)/7;
forprime(n=3,10^5,if(ispseudoprime(f(n)),print1(n,", ")))
/* Joerg Arndt, Mar 27 2011 */

Extensions

3 more terms from Emeric Deutsch, Feb 17 2007
2 more terms from Farideh Firoozbakht, Apr 16 2007
Two more terms (13463 and 23929) found by Lelio R Paula in 2008 corresponding to probable primes with 8105 and 14406 digits. Jean-Louis Charton, Oct 06 2010
Two more terms (81223 and 121271) found by Jean-Louis Charton in March 2011 corresponding to probable primes with 48901 and 73012 digits

A128071 Numbers k such that (3^k + 13^k)/16 is prime.

Original entry on oeis.org

3, 7, 127, 2467, 3121, 34313
Offset: 1

Views

Author

Alexander Adamchuk, Feb 14 2007

Keywords

Comments

All terms are primes.
a(4) is certified prime by primo; a(5) is a probable prime. - Ray G. Opao, Aug 02 2007
a(7) > 10^5. - Robert Price, Apr 14 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, A128069, A128070, 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=13; 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+13^n)/16) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

One more term from Ray G. Opao, Aug 02 2007
a(6) from Robert Price, Apr 14 2013

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

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

A221637 Numbers n such that (15^n + 14^n)/29 is prime.

Original entry on oeis.org

3, 127, 227, 1009, 1951, 5101, 14011
Offset: 1

Views

Author

Robert Price, May 28 2013

Keywords

Comments

All terms are prime.
a(8) > 10^5.

Crossrefs

Cf. A057180, A128072, A128343, A181141, A187819, A217095, A185239, A213216, A225191, A225097.

Programs

  • Mathematica
    Select[ Prime[ Range[1, 100000] ], PrimeQ[ (15^# + 14^#)/29 ]& ]
  • PARI
    is(n)=ispseudoprime((15^n+14^n)/29) \\ Charles R Greathouse IV, Feb 20 2017

A224984 Numbers n such that (14^n + 13^n)/27 is prime.

Original entry on oeis.org

7, 13, 311, 1637, 4363, 10433, 41669, 45631
Offset: 1

Views

Author

Robert Price, Apr 22 2013

Keywords

Comments

All terms are prime.
a(9) > 10^5.

Crossrefs

Cf. A057180, A128072, A128343, A181141, A187819, A217095, A185239, A213216.

Programs

  • Mathematica
    Select[ Prime[ Range[1, 100000] ], PrimeQ[ (14^# + 13^#)/27 ]& ]
  • PARI
    forprime(p=3,10^6, if(ispseudoprime((14^p + 13^p)/27), print1(p,", ") ) ); \\ Joerg Arndt, Jul 29 2013

Extensions

Removed incorrect first term of "2".
Showing 1-10 of 10 results.

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

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