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 17 results. Next

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

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

A227170 Numbers n such that (16^n + 15^n)/31 is prime.

Original entry on oeis.org

3, 5, 13, 1439, 1669, 37691
Offset: 1

Views

Author

Jean-Louis Charton, Jul 03 2013

Keywords

Comments

All terms are prime.
a(7) > 10^5. - Robert Price, Aug 26 2013

Crossrefs

Cf. A000978, A057469, A128066, A128335, A128336, A187805, A181141, A187819, A217095.

Programs

A247244 Smallest prime p such that (n^p + (n+1)^p)/(2n+1) is prime, or -1 if no such p exists.

Original entry on oeis.org

3, 3, 3, 5, 3, 3, 7, 3, 7, 53, 47, 3, 7, 3, 3, 41, 3, 5, 11, 3, 3, 11, 11, 3, 5, 103, 3, 37, 17, 7, 13, 37, 3, 269, 17, 5, 17, 3, 5, 139, 3, 11, 78697, 5, 17, 3671, 13, 491, 5, 3, 31, 43, 7, 3, 7, 2633, 3, 7, 3, 5, 349, 3, 41, 31, 5, 3, 7, 127, 3, 19, 3, 11, 19, 101, 3, 5, 3, 3
Offset: 1

Views

Author

Eric Chen, Nov 28 2014

Keywords

Comments

All terms are odd primes.
a(79) > 10000, if it exists.
a(80)..a(93) = {3, 7, 13, 7, 19, 31, 13, 163, 797, 3, 3, 11, 13, 5}, a(95)..a(112) = {5, 2657, 19, 787, 3, 17, 3, 7, 11, 1009, 3, 61, 53, 2371, 5, 3, 3, 11}, a(114)..a(126) = {103, 461, 7, 3, 13, 3, 7, 5, 31, 41, 23, 41, 587}, a(128)..a(132) = {7, 13, 37, 3, 23}, a(n) is currently unknown for n = {79, 94, 113, 127, 133, ...} (see the status file under Links).

Examples

			a(10) = 53 because (10^p + 11^p)/21 is composite for all p < 53 and prime for p = 53.

Links

Crossrefs

Cf. A058013, A125713, A000978, A057469, A128066, A128335, A128336, A187805, A181141, A187819, A217095, A185239, A213216, A225097, A224984, A221637, A227170, A228573, A227171, A225818, A227172, A227173, A227174.

Programs

  • Mathematica
    lmt = 4200; f[n_] := Block[{p = 2}, While[p < lmt && !PrimeQ[((n + 1)^p + n^p)/(2n + 1)], p = NextPrime@ p]; If[p > lmt, 0, p]]; Do[Print[{n, f[n] // Timing}], {n, 1000}] (* Robert G. Wilson v, Dec 01 2014 *)
  • PARI
    a(n)=forprime(p=3, , if(ispseudoprime((n^p+(n+1)^p)/(2*n+1)), return(p)))

Formula

a(n) = 3 if and only if n^2 + n + 1 is a prime (A002384).

Extensions

a(43) from Aurelien Gibier, Nov 27 2023
Showing 1-10 of 17 results. Next

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