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 14 results. Next

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

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

A130652 a(n) = 11^n - 2.

Original entry on oeis.org

9, 119, 1329, 14639, 161049, 1771559, 19487169, 214358879, 2357947689, 25937424599, 285311670609, 3138428376719, 34522712143929, 379749833583239, 4177248169415649, 45949729863572159, 505447028499293769, 5559917313492231479, 61159090448414546289, 672749994932560009199
Offset: 1

Views

Author

Alexander Adamchuk, Jun 20 2007

Keywords

Comments

There are only two known primes in a(n): a(4) = 14639 and a(6) = 1771559 (see A128472 = smallest prime of the form (2n-1)^k - 2 for k > (2n-1), or 0 if no such number exists). 3 divides a(2k-1). 7 divides a(3k-1). 13 divides a(12k-5). 17 divides a(16k-14).
Final digit of a(n) is 9.
Final two digits of a(n) are periodic with period 10: a(n) mod 100 = {09, 19, 29, 39, 49, 59, 69, 79, 89, 99}.
Final three digits of a(n) are periodic with period 50: a(n) mod 1000 = {009, 119, 329, 639, 049, 559, 169, 879, 689, 599, 609, 719, 929, 239, 649, 159, 769, 479, 289, 199, 209, 319, 529, 839, 249, 759, 369, 079, 889, 799, 809, 919, 129, 439, 849, 359, 969, 679, 489, 399, 409, 519, 729, 039, 449, 959, 569, 279, 089, 999}.

Links

Crossrefs

Cf. A001020, A024127, A034524. Cf. A104096 = Largest prime <= 11^n. Cf. A084714 = smallest prime of the form (2n-1)^k - 2, or 0 if no such number exists. Cf. A128472 = smallest prime of the form (2n-1)^k - 2 for k>(2n-1), or 0 if no such number exists. Cf. A014224, A109080, A090669, A128455, A128457, A128458, A128459, A128460, A128461.

Programs

  • Magma
    [11^n - 2: n in [1..50]]; // Vincenzo Librandi, Jun 08 2011
  • Mathematica
    LinearRecurrence[{12, -11},{9, 119},17] (* Ray Chandler, Aug 26 2015 *)

Formula

a(n) = 11*a(n-1) + 20; a(1)=9. - Vincenzo Librandi, Jun 08 2011
From Elmo R. Oliveira, Jun 16 2025: (Start)
G.f.: x*(11*x+9)/((11*x-1)*(x-1)).
E.g.f.: 1 + exp(x)*(exp(10*x) - 2).
a(n) = 12*a(n-1) - 11*a(n-2) for n > 2. (End)

A133858 Primes of the form 11^k - 2.

Original entry on oeis.org

14639, 1771559
Offset: 1

Views

Author

Alexander Adamchuk, Sep 27 2007

Keywords

Comments

Last digit of all terms is 9.
The nest term (11^22420-2) is too large to be displayed; see A133982 for the corresponding k. - Joerg Arndt, Nov 28 2020

Examples

			a(1) = 11^4 - 2 = 14639,
a(2) = 11^6 - 2 = 1771559.

Crossrefs

Cf. A104096 (largest prime <= 11^n), A130652, A128472, A084714 (smallest prime of the form (2n-1)^k - 2).
Cf. A014224, A109080, A090669, A128455, A133982, A128457, A128458, A128459, A128460, A128461.

A155899 Square matrix T(m,n)=1 if (2m+1)^(2n-1)-2 is prime, 0 otherwise; read by antidiagonals.

Original entry on oeis.org

0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0
Offset: 1

Views

Author

M. F. Hasler, Feb 01 2009

Keywords

Comments

In some sense the "minimal" possible generalization of the pattern of Mersenne primes (cf. A000043) is to consider powers of odd numbers minus 2. Here only odd powers are considered.

Crossrefs

Cf. A084714, A128472, A014224, A109080, A090669, A128455, A128457, A128458, A128459, A128460, A128461.

Programs

  • PARI
    T = matrix( 19,19,m,n, isprime((2*m+1)^(2*n-1)-2)) ;
A155899 = concat( vector( vecmin( matsize(T)), i, vector( i, j, T[j,i-j+1])))

A133856 Least number k > (2n-1) such that (2n-1)^k - 2 is prime, or 0 if no such number exists.

Original entry on oeis.org

0, 4, 14, 8, 11, 22420, 78, 17, 24, 20, 25, 24, 63, 30, 42, 69, 128, 50, 119, 204, 2816, 76, 52, 288, 64, 66, 184, 153, 67, 268, 78, 210, 438, 295, 96, 74, 136, 128, 2900, 1898, 130, 92, 381, 106, 18626, 97, 98, 1650, 747, 109, 214, 113, 312, 354, 1702, 560, 2798, 123, 171, 554, 11210, 834, 208, 990, 9271
Offset: 1

Views

Author

Alexander Adamchuk, Oct 01 2007

Keywords

Comments

a(66) > 40000. - Robert Price, Mar 02 2015

Links

Crossrefs

Cf. A128472 (smallest prime of the form (2n-1)^k - 2 for k > (2n-1), or 0 if no such number exists).
Cf. A084714 (smallest prime of the form (2n-1)^k - 2, or 0 if no such number exists).
Cf. A014224, A109080, A090669, A128455, A128457, A128458, A128459, A128460, A128461.
Cf. A133858, A133982.

Formula

A128472(n) = (2n-1)^a(n) - 2 for n > 1.

Extensions

a(6) = 22420 was found by Rick L. Shepherd, Sep 29 2009
a(21)-a(44) from Max Alekseyev, Oct 04 2007
a(45)-a(65) from Robert Price, Mar 02 2015
Showing 1-10 of 14 results. Next

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