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 25 results. Next

A128457 Numbers k such that 13^k - 2 is a prime.

Original entry on oeis.org

1, 2, 4, 5, 12, 78, 80, 90, 117, 120, 813, 1502, 2306, 2946, 6308, 13320, 26369, 31868, 44265, 81008
Offset: 1

Views

Author

Alexander Adamchuk, Mar 14 2007

Keywords

Comments

13320 is a term found by Lelio R Paula 11/2006.
Numbers corresponding to a(13)..a(16) are probable primes. If n is of the form 4k+3 then 13^n-2 is composite, because 13^n-2 == (3^4)^k*3^3 - 2 == 25 == 0 (mod 5). So there is no term of the form 4k+3. - Farideh Firoozbakht, Dec 07 2009
a(21) > 2*10^5. - Robert Price, Oct 03 2014

Crossrefs

Cf. A084714 (smallest prime of the form (2n-1)^k - 2).
Cf. A128472 (smallest prime of the form (2n-1)^k - 2 for k > (2n-1)).
Cf. A014224, A109080, A090669, A128455, A128458, A128459, A128460, A128461.

Programs

  • Mathematica
    Do[ f = 13^n - 2; If[ PrimeQ[ f ], Print[ {n, f} ] ], {n,1,1000} ]

Extensions

813 from Stefan Steinerberger, May 05 2007
a(12) from M. F. Hasler, Feb 07 2009
a(13)-a(16) from Farideh Firoozbakht, Dec 07 2009
a(17)-a(20) from Robert Price, Oct 03 2014

A128459 Numbers k such that 17^k - 2 is a prime.

Original entry on oeis.org

6, 24, 30, 106, 184, 232, 460, 1258, 3480, 5458, 32886
Offset: 1

Views

Author

Alexander Adamchuk, Mar 14 2007

Keywords

Comments

No more terms through 50000. - Ryan Propper, Dec 06 2008
a(12) > 2*10^5. - Robert Price, Oct 23 2014

Crossrefs

Cf. A084714 (smallest prime of the form (2n-1)^k - 2).
Cf. A128472 (smallest prime of the form (2n-1)^k - 2 for k > (2n-1)).
Cf. A014224, A109080, A090669, A128455, A128457, A128458, A128460, A128461.

Programs

  • Mathematica
    Do[ f = 17^n - 2; If[ PrimeQ[ f ], Print[ {n, f} ] ], {n,1,1000} ]

Extensions

2 more terms from Stefan Steinerberger, May 05 2007
Two more terms from Ryan Propper, Jan 16 2008
One more term from Ryan Propper, Dec 06 2008

A128460 Numbers k such that 19^k - 2 is a prime.

Original entry on oeis.org

1, 2, 3, 13, 14, 19, 20, 23, 38, 1124, 7592, 11755, 12155, 12915, 14172, 15500, 20255, 28388, 184650
Offset: 1

Views

Author

Alexander Adamchuk, Mar 14 2007

Keywords

Comments

No more terms through 50000. - Ryan Propper, Dec 04 2008
a(20) > 2*10^5. - Robert Price, Oct 22 2014

Crossrefs

Cf. A084714 (smallest prime of the form (2n-1)^k - 2).
Cf. A128472 (smallest prime of the form (2n-1)^k - 2 for k > (2n-1)).
Cf. A014224, A109080, A090669, A128455, A128457, A128458, A128459, A128461.

Programs

  • Magma
    [n: n in [0..1000] | IsPrime(19^n-2)]; // Vincenzo Librandi, Oct 23 2014
  • Mathematica
    Do[ f = 19^n - 2; If[ PrimeQ[ f ], Print[ {n, f} ] ], {n,1,1000} ]

Extensions

1124 from Stefan Steinerberger, May 05 2007
7592 from Ryan Propper, Dec 31 2007
Additional terms from Ryan Propper, Dec 04 2008
a(19) from Robert Price, Oct 22 2014

A128455 Numbers k such that 9^k - 2 is a prime.

Original entry on oeis.org

1, 2, 3, 11, 45, 51, 260, 324, 390, 393, 1112, 3092, 4445, 10373, 15861, 18528, 97715, 112961
Offset: 1

Views

Author

Alexander Adamchuk, Mar 14 2007

Keywords

Comments

a(19) > 2*10^5. - Robert Price, Aug 18 2014

Crossrefs

Cf. A084714 (smallest prime of the form (2n-1)^k - 2).
Cf. A128472 (smallest prime of the form (2n-1)^k - 2 for k>(2n-1)).
Cf. A014224, A109080, A090669, A128457, A128458, A128459, A128460, A128461.

Programs

  • Mathematica
    Do[ f = 9^n - 2; If[ PrimeQ[ f ], Print[ {n, f} ] ], {n,1,1000} ]

Extensions

1112 from Stefan Steinerberger, May 05 2007
More terms from Ryan Propper, Jan 12 2008
a(15)-a(18) from Robert Price, Aug 18 2014

A128458 Numbers k such that 15^k - 2 is a prime.

Original entry on oeis.org

1, 2, 3, 7, 12, 17, 19, 51, 65, 550, 1460, 1641, 7035, 18002, 20963, 21163, 42563, 94906, 148048
Offset: 1

Views

Author

Alexander Adamchuk, Mar 14 2007

Keywords

Comments

a(20) > 2*10^5. - Robert Price, Jun 23 2015

Crossrefs

Cf. A084714 (smallest prime of the form (2n-1)^k - 2).
Cf. A128472 (smallest prime of the form (2n-1)^k - 2 for k > (2n-1)).
Cf. A014224, A109080, A090669, A128455, A128457, A128459, A128460, A128461.

Programs

  • Mathematica
    Do[ f = 15^n - 2; If[ PrimeQ[ f ], Print[ {n, f} ] ], {n,1,1000} ]
Do[If[PrimeQ[15^n - 2], Print[n]], {n, 10^4}] (* Ryan Propper, Jun 06 2007 *)

Extensions

550 from Stefan Steinerberger, May 05 2007
3 more terms from Ryan Propper, Jun 06 2007
a(14)-a(19) from Robert Price, Jun 23 2015

A128472 a(n) is the smallest prime of the form (2n-1)^k - 2 for k > (2n-1), or 0 if no such number exists.

Original entry on oeis.org

0, 79, 6103515623, 5764799, 31381059607
Offset: 1

Views

Author

Alexander Adamchuk, Mar 14 2007, Oct 01 2007

Keywords

Comments

a(6) = 11^22420 - 2 was found by Rick L. Shepherd on Sep 29 2007. It has 23349 decimal digits and it is too large to include.
a(7) through a(12): {771936328432730777189183517369830159827426282764863750131729657829597399846468418688727, 98526125335693359373, 339448671314611904643504117119, 37589973457545958193355599, 1136272165922724266740722458520499, 480250763996501976790165756943039}.

Links

Crossrefs

Cf. A084714 (smallest prime of the form (2n-1)^k - 2).
Cf. A133856 (least number k > (2n-1) such that (2n-1)^k - 2 is prime).
Cf. A014224, A109080, A090669, A128455, A128457, A128458, A128459, A128460, A128461.
Cf. A133858, A133982.

Extensions

Edited by Max Alekseyev, Sep 18 2009

A096305 Numbers k such that 7^k + 4 is prime.

Original entry on oeis.org

0, 1, 2, 3, 5, 7, 9, 14, 23, 129, 198, 235, 275, 630, 870, 1033, 1290, 3293, 3458, 11466, 13885, 25893, 32186, 33139, 58125, 78929, 97197, 121933, 128422, 442674
Offset: 1

Views

Author

Herman H. Rosenfeld (herm3(AT)pacbell.net), Jun 26 2004

Keywords

Examples

			7^14 + 4 = 678223072853 is a prime number.

Crossrefs

Cf. A236371, A217131, A191469, A090669, A096305, A217130, A217132, A152213.

Programs

  • Mathematica
    Do[If[PrimeQ[7^n+4], Print[n]], {n, 1, 1000}]
  • PARI
    for(n=0, 10^5, if(ispseudoprime(7^n+4), print1(n, ", "))) \\  Felix Fröhlich, Jun 04 2014

Extensions

More terms (probable primes) from Rick L. Shepherd, Jun 29 2004
7 more terms from Jason Earls, Feb 16 2008
a(25)-a(27) from Robert Price, Jan 24 2014
a(28)-a(29) from Lelio R. Paula, Nov 2014
a(30) from Paul Bourdelais, Feb 11 2021

A128461 Numbers k such that 21^k - 2 is a prime.

Original entry on oeis.org

1, 2, 4, 10, 21, 25, 27, 32, 60, 88, 106, 120, 146, 264, 828, 965, 1944, 4822, 12089, 14427, 17354, 42335, 46395, 58348, 190632
Offset: 1

Views

Author

Alexander Adamchuk, Mar 14 2007

Keywords

Comments

a(26) > 2*10^5. - Robert Price, Jul 14 2015

Crossrefs

Cf. A084714 (smallest prime of the form (2n-1)^k - 2).
Cf. A128472 (smallest prime of the form (2n-1)^k - 2 for k > (2n-1)).
Cf. A014224, A109080, A090669, A128455, A128457, A128458, A128459, A128460.

Programs

  • Mathematica
    Do[ f = 21^n - 2; If[ PrimeQ[ f ], Print[ {n, f} ] ], {n,1,1000} ]

Extensions

2 more terms from Stefan Steinerberger, May 05 2007
a(17)-a(25) from Robert Price, Jul 14 2015

A191469 Numbers n such that 7^n - 6 is prime.

Original entry on oeis.org

2, 3, 6, 9, 21, 25, 33, 49, 54, 133, 245, 255, 318, 1023, 1486, 3334, 6821, 8555, 11605, 42502, 44409, 90291, 92511, 140303
Offset: 1

Views

Author

Vincenzo Librandi, Jun 06 2011

Keywords

Comments

a(14)=1023 and a(15)=1486 correspond to BPSW strong probable primes (passing PARI's ispseudoprime()). - Joerg Arndt, Jun 06 2011
a(25) > 2*10^5. - Robert Price, Nov 14 2014

Crossrefs

Cf. A014224, A059266, A059613, A059614, A095714, A177093.
Cf. A236371, A217131, A191469, A090669, A096305, A217130, A217132, A152213.

Programs

  • Magma
    [n: n in [1..1000]| IsPrime(7^n-6)]
  • Maple
    A191469:=n->`if`(isprime(7^n-6),n,NULL): seq(A191469(n), n=1..10^3); # Wesley Ivan Hurt, Nov 14 2014
  • Mathematica
    Select[Range[1,5000],PrimeQ[7^#-6]&] (* Vincenzo Librandi, Aug 05 2012 *)
  • PARI
    for(n=1, 10^6, if(isprime(7^n-6), print1(n, ", ")))

Extensions

a(17)-a(23) from Robert Price, Jan 24 2014
a(24) from Robert Price, Nov 14 2014

A217130 Numbers n such that 7^n + 6 is prime.

Original entry on oeis.org

0, 1, 3, 16, 36, 244, 315, 2577, 9500, 17596, 25551, 32193, 32835, 36504, 75136
Offset: 1

Views

Author

Vincenzo Librandi, Oct 01 2012

Keywords

Comments

a(16) > 10^5. - Robert Price, Jan 24 2014

Crossrefs

Cf. A236371, A217131, A191469, A090669, A096305, A217130, A217132, A152213.

Programs

  • Magma
    /* The code produces the sequence up to 315: */ [n: n in [0..2000] | IsPrime(7^n+6)];
  • Mathematica
    Select[Range[0, 5000], PrimeQ[7^# + 6] &]
  • PARI
    for(n=1, 5000, if(isprime(7^n+6), print1(n", ")))

Extensions

a(9)-a(15) from Robert Price, Jan 24 2014
Showing 1-10 of 25 results. Next

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

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