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 46 results. Next

A057735 Primes of the form 3^k + 2.

Original entry on oeis.org

3, 5, 11, 29, 83, 6563, 59051, 4782971, 14348909, 282429536483, 2541865828331, 150094635296999123, 1144561273430837494885949696429, 57264168970223481226273458862846808078011946891, 30432527221704537086371993251530170531786747066637051
Offset: 1

Views

Author

G. L. Honaker, Jr., Oct 29 2000

Keywords

Links

Crossrefs

Cf. A000040, A051783 (corresponding k's).

Programs

Formula

a(n) = 3^A051783(n) + 2. - Elmo R. Oliveira, Nov 09 2023

A217137 Numbers k such that 3^k + 10 is prime.

Original entry on oeis.org

0, 1, 2, 3, 6, 8, 18, 36, 98, 114, 134, 138, 212, 252, 516, 1166, 2321, 2442, 2732, 4569, 8622, 8709, 16487, 22722, 25242, 29928, 32034, 33783, 34001, 44934, 50868, 77861, 90188, 102102, 171843, 178226, 273521
Offset: 1

Views

Author

Vincenzo Librandi, Oct 01 2012

Keywords

Comments

a(37) > 2*10^5. - Robert Price, Oct 23 2013
a(38) > 3*10^5. - Tyler NeSmith, Jan 16 2021

Crossrefs

Cf. A014224, A051783, A058958, A058959, A102907.

Programs

  • Mathematica
    Select[Range[0, 5000], PrimeQ[3^# + 10] &]
  • PARI
    for(n=0, 5*10^3, if(isprime(3^n+10), print1(n", ")))

Extensions

a(21)-a(36) from Robert Price, Oct 23 2013
a(37) from Tyler NeSmith, Jan 16 2021

A217347 Numbers k such that 3^k - 10 is prime.

Original entry on oeis.org

3, 4, 5, 6, 8, 17, 18, 21, 22, 36, 38, 41, 54, 56, 81, 92, 100, 106, 160, 310, 406, 560, 902, 5549, 9926, 12334, 19374, 19995, 20166, 39609, 62900, 186903, 244461
Offset: 1

Views

Author

Vincenzo Librandi, Oct 01 2012

Keywords

Comments

a(33) > 2*10^5. - Robert Price, Sep 07 2013
a(34) > 3*10^5. - Tyler NeSmith, Oct 03 2022

Crossrefs

Cf. A014224, A051783, A058958, A058959.

Programs

  • Magma
    /* The code produces the sequence up to 560: */ [n: n in [2..800] | IsPrime(3^n - 10)];
  • Mathematica
    Select[Range[2, 5000], PrimeQ[3^# - 10] &]
  • PARI
    for(n=2, 5*10^3, if(isprime(3^n-10), print1(n", ")))

Extensions

a(24)-a(32) from Robert Price, Sep 07 2013
a(33) from Tyler NeSmith, Oct 03 2022

A205647 Numbers k such that 3^k + 16 is prime.

Original entry on oeis.org

0, 1, 3, 4, 7, 8, 9, 12, 13, 15, 27, 31, 49, 57, 60, 75, 139, 147, 283, 327, 488, 604, 700, 825, 908, 1051, 1064, 1215, 5319, 9669, 10136, 16675, 25656, 28933, 35864, 47671, 68028, 73380, 186223, 194965, 221649, 233059, 240644, 513007, 543128, 551491, 648872, 989124, 994536
Offset: 1

Views

Author

Jonathan Vos Post, Jan 30 2012

Keywords

Comments

Indices of primes in A205646.
a(50) > 10^6. - Robert Price, Oct 28 2020

Examples

			57 is in the sequence because (3^57) + 16 = 1570042899082081611640534579 is prime.

Crossrefs

Cf. Sequences of numbers k such that 3^k + m is prime:
(m = 2) A051783, (m = -2) A014224, (m = 4) A058958, (m = -4) A058959,
(m = 8) A217136, (m = -8) A217135, (m = 10) A217137, (m = -10) A217347,
(m = 14) A219035, (m = -14) A219038, (m = 16) A205647, (m = -16) A219039,
(m = 20) A219040, (m = -20) A219041, (m = 22) A219042, (m = -22) A219043,
(m = 26) A219044, (m = -26) A219045, (m = 28) A219046, (m = -28) A219047,
(m = 32) A219048, (m = -32) A219049, (m = 34) A219050, (m = -34) A219051. Note that if m is a multiple of 3, 3^k + m is also a multiple of 3 (for k greater than 0), and as such isn't prime.

Programs

Formula

{n: 3^n + 16 is in A000040} = {n: 3^n + 16 is prime} = {n: A000244(n) is prime} = {n: A205646(n) is prime}.

Extensions

5319 from Nicolas M. Perrault, Nov 10 2012
a(30)-a(40) from Robert Price, Oct 23 2013
a(41) discovered by Lelio R Paula, Nov 2016
a(42)-a(43) from Robert Price, Apr 02 2020
a(44)-a(46) from Robert Price, May 14 2020
a(47)-a(49) from Robert Price, Oct 28 2020

A217136 Numbers k such that 3^k + 8 is prime.

Original entry on oeis.org

1, 2, 4, 5, 8, 13, 14, 20, 38, 44, 77, 88, 124, 152, 244, 557, 2429, 4382, 6268, 18488, 75097, 81998, 96460, 143497
Offset: 1

Views

Author

Vincenzo Librandi, Oct 01 2012

Keywords

Comments

a(25) > 2*10^5. - Robert Price, Sep 25 2013

Crossrefs

Cf. A014224, A051783, A058958, A058959.

Programs

  • Mathematica
    Select[Range[0, 5000], PrimeQ[3^# + 8] &]
  • PARI
    for(n=1, 5*10^3, if(isprime(3^n+8), print1(n", ")))

Extensions

a(19)-a(24) from Robert Price, Sep 25 2013

A217135 Numbers k such that 3^k - 8 is prime.

Original entry on oeis.org

3, 4, 7, 8, 14, 20, 22, 62, 139, 254, 272, 430, 907, 1906, 2278, 2827, 3598, 6812, 15266, 20915, 26180, 26342, 27022, 48275, 65186, 69247, 86647
Offset: 1

Views

Author

Vincenzo Librandi, Oct 01 2012

Keywords

Comments

a(28) > 2*10^5. - Robert Price, Sep 02 2013

Crossrefs

Cf. A014224, A051783, A058958, A058959.

Programs

  • Mathematica
    Select[Range[2, 5000], PrimeQ[3^# - 8] &]
  • PARI
    for(n=2, 5*10^3, if(isprime(3^n-8), print1(n", ")))

Extensions

a(18)-a(27) from Robert Price, Sep 02 2013

A219035 Numbers k such that 3^k + 14 is prime.

Original entry on oeis.org

1, 2, 3, 5, 6, 9, 10, 25, 98, 122, 153, 190, 258, 511, 549, 1703, 1790, 1870, 2418, 5226, 5258, 5626, 8550, 13174, 16718, 23669, 25215, 33447, 182566, 188286
Offset: 1

Views

Author

Nicolas M. Perrault, Nov 10 2012

Keywords

Comments

a(31) > 2*10^5. - Robert Price, Sep 27 2013

Crossrefs

Cf. Sequences of numbers k such that 3^k + m is prime:
(m = 2) A051783, (m = -2) A014224, (m = 4) A058958, (m = -4) A058959,
(m = 8) A217136, (m = -8) A217135, (m = 10) A217137, (m = -10) A217347,
(m = 14) A219035, (m = -14) A219038, (m = 16) A205647, (m = -16) A219039,
(m = 20) A219040, (m = -20) A219041, (m = 22) A219042, (m = -22) A219043,
(m = 26) A219044, (m = -26) A219045, (m = 28) A219046, (m = -28) A219047,
(m = 32) A219048, (m = -32) A219049, (m = 34) A219050, (m = -34) A219051. Note that if m is a multiple of 3, 3^k + m is also a multiple of 3 (for k greater than 0), and as such isn't prime.

Programs

  • Mathematica
    Do[If[PrimeQ[3^n + 14], Print[n]], {n, 0, 10000}]
  • PARI
    is(n)=isprime(3^n+14) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(24)-a(30) from Robert Price, Sep 27 2013

A219038 Numbers k such that 3^k - 14 is prime.

Original entry on oeis.org

3, 4, 5, 8, 17, 19, 29, 124, 304, 640, 1205, 1549, 1805, 2492, 2945, 13075, 20237, 102763, 173755, 173828, 174040
Offset: 1

Views

Author

Nicolas M. Perrault, Nov 10 2012

Keywords

Comments

a(22) > 2*10^5. - Robert Price, Aug 31 2013

Crossrefs

Cf. Sequences of numbers k such that 3^k + m is prime:
(m = 2) A051783, (m = -2) A014224, (m = 4) A058958, (m = -4) A058959,
(m = 8) A217136, (m = -8) A217135, (m = 10) A217137, (m = -10) A217347,
(m = 14) A219035, (m = -14) A219038, (m = 16) A205647, (m = -16) A219039,
(m = 20) A219040, (m = -20) A219041, (m = 22) A219042, (m = -22) A219043,
(m = 26) A219044, (m = -26) A219045, (m = 28) A219046, (m = -28) A219047,
(m = 32) A219048, (m = -32) A219049, (m = 34) A219050, (m = -34) A219051. Note that if m is a multiple of 3, 3^k + m is also a multiple of 3 (for k greater than 0), and as such isn't prime.

Programs

  • Mathematica
    Do[If[PrimeQ[3^n - 14], Print[n]], {n, 3, 3000}]
Select[Range[1000], PrimeQ[3^# - 14] &] (* Alonso del Arte, Nov 10 2012 *)
  • PARI
    is(n)=isprime(3^n-14) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(16)-a(21) from Robert Price, Aug 31 2013

A219040 Numbers k such that 3^k + 20 is prime.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 8, 10, 11, 14, 44, 55, 68, 71, 80, 123, 158, 213, 220, 272, 668, 725, 885, 1132, 1677, 2056, 2618, 3130, 3986, 6027, 8660, 11582, 12278, 14054, 62956, 103431, 120434, 123890, 181407
Offset: 1

Views

Author

Nicolas M. Perrault, Nov 10 2012

Keywords

Comments

a(40) > 2*10^5. - Robert Price, Oct 20 2013

Examples

			3^3 + 20 = 47 (prime), so 3 is in the sequence.

Crossrefs

Cf. Sequences of numbers k such that 3^k + m is prime:
(m = 2) A051783, (m = -2) A014224, (m = 4) A058958, (m = -4) A058959,
(m = 8) A217136, (m = -8) A217135, (m = 10) A217137, (m = -10) A217347,
(m = 14) A219035, (m = -14) A219038, (m = 16) A205647, (m = -16) A219039,
(m = 20) A219040, (m = -20) A219041, (m = 22) A219042, (m = -22) A219043,
(m = 26) A219044, (m = -26) A219045, (m = 28) A219046, (m = -28) A219047,
(m = 32) A219048, (m = -32) A219049, (m = 34) A219050, (m = -34) A219051. Note that if m is a multiple of 3, 3^k + m is also a multiple of 3 (for k greater than 0), and as such isn't prime.

Programs

  • Mathematica
    Do[If[PrimeQ[3^n + 20], Print[n]], {n, 10000}]
  • PARI
    is(n)=isprime(3^n+20) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(32)-a(39) from Robert Price, Oct 20 2013

A219041 Numbers k such that 3^k - 20 is prime.

Original entry on oeis.org

3, 4, 5, 6, 10, 11, 19, 20, 23, 25, 26, 71, 80, 91, 101, 139, 150, 179, 200, 246, 599, 626, 1126, 2215, 4189, 7795, 30626, 66941, 87630, 104388
Offset: 1

Views

Author

Nicolas M. Perrault, Nov 10 2012

Keywords

Comments

a(31) > 2*10^5. - Robert Price, Nov 14 2013

Examples

			3^3 - 20 = 7 (prime), so 3 is in the sequence.

Crossrefs

Cf. Sequences of numbers k such that 3^k + m is prime:
(m = 2) A051783, (m = -2) A014224, (m = 4) A058958, (m = -4) A058959,
(m = 8) A217136, (m = -8) A217135, (m = 10) A217137, (m = -10) A217347,
(m = 14) A219035, (m = -14) A219038, (m = 16) A205647, (m = -16) A219039,
(m = 20) A219040, (m = -20) A219041, (m = 22) A219042, (m = -22) A219043,
(m = 26) A219044, (m = -26) A219045, (m = 28) A219046, (m = -28) A219047,
(m = 32) A219048, (m = -32) A219049, (m = 34) A219050, (m = -34) A219051. Note that if m is a multiple of 3, 3^k + m is also a multiple of 3 (for k greater than 0), and as such isn't prime.

Programs

  • Mathematica
    Do[If[PrimeQ[3^n - 20], Print[n]], {n, 3, 10000}]
  • PARI
    is(n)=isprime(3^n-20) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(27)-a(30) from Robert Price, Nov 14 2013
Showing 1-10 of 46 results. Next

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

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