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 15 results. Next

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

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

A219043 Numbers k such that 3^k - 22 is prime.

Original entry on oeis.org

3, 4, 9, 13, 28, 45, 46, 184, 285, 688, 697, 1257, 1785, 2368, 3721, 7444, 51613
Offset: 1

Views

Author

Nicolas M. Perrault, Nov 10 2012

Keywords

Comments

a(18) > 2*10^5. - Robert Price, Oct 18 2013

Examples

			3^3 - 22 = 5 (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 - 22], Print[n]], {n, 10000}]
  • PARI
    is(n)=isprime(3^n-22) \\ Charles R Greathouse IV, Feb 17 2017
  • Python
    from sympy import isprime
def ok(n): return isprime(3**n - 22)
print([m for m in range(700) if ok(m)]) # Michael S. Branicky, Mar 04 2021

Extensions

a(17) from Robert Price, Oct 18 2013

A219044 Numbers k such that 3^k + 26 is prime.

Original entry on oeis.org

1, 3, 4, 5, 7, 9, 11, 16, 24, 28, 49, 53, 63, 88, 137, 184, 217, 299, 300, 732, 815, 999, 1243, 1320, 1397, 1668, 2109, 2681, 4973, 5513, 12100, 14284, 14592, 35812, 38559, 49687, 53167, 66907, 88765, 98251, 113548, 137988, 139432, 148008
Offset: 1

Views

Author

Nicolas M. Perrault, Nov 10 2012

Keywords

Comments

a(45) > 2*10^5. - Robert Price, Nov 29 2013

Examples

			3^3 + 26 = 53 (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 + 26], Print[n]], {n, 10000}]
  • PARI
    is(n)=isprime(3^n+26) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(31)-a(44) from Robert Price, Nov 29 2013

A219045 Numbers k such that 3^k - 26 is prime.

Original entry on oeis.org

7, 10, 13, 22, 27, 30, 57, 62, 117, 255, 535, 651, 873, 998, 1502, 18145, 22766, 25770, 43558, 45663, 48058, 62887, 87477, 103585, 115802
Offset: 1

Views

Author

Nicolas M. Perrault, Nov 10 2012

Keywords

Comments

a(26) > 2*10^5. - Robert Price, Nov 20 2013

Examples

			3^7 - 26 = 2161 (prime), so 7 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 - 26], Print[n]], {n, 3, 10000}]
  • PARI
    is(n)=isprime(3^n-26) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(16)-a(25) from Robert Price, Nov 20 2013

A219046 Numbers k such that 3^k + 28 is prime.

Original entry on oeis.org

1, 2, 4, 5, 6, 10, 14, 16, 25, 50, 54, 66, 76, 109, 124, 129, 154, 201, 210, 225, 324, 844, 1444, 2529, 3029, 3292, 3340, 9162, 44721, 45662, 114085, 197542
Offset: 1

Views

Author

Nicolas M. Perrault, Nov 10 2012

Keywords

Comments

a(33) > 2*10^5. - Robert Price, Nov 12 2013

Examples

			3^2 + 28 = 37 and 37 is prime, so 2 is a term.

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 + 28], Print[n]], {n, 10000}]
  • PARI
    is(n)=isprime(3^n+28) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(29)-a(32) from Robert Price, Nov 12 2013

A219047 Numbers k such that 3^k - 28 is prime.

Original entry on oeis.org

4, 6, 10, 15, 22, 24, 27, 35, 63, 91, 95, 96, 124, 132, 220, 280, 338, 372, 432, 568, 692, 738, 1144, 1168, 1698, 2080, 2138, 2710, 2895, 2984, 3536, 3816, 4462, 4972, 6588, 6666, 10350, 58991, 68854, 145806, 163500, 196192
Offset: 1

Views

Author

Nicolas M. Perrault, Nov 10 2012

Keywords

Comments

a(43) > 2*10^5. - Robert Price, Dec 10 2013

Examples

			3^4 - 28 = 53 (prime), so 4 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 - 28], Print[n]], {n, 10000}]
  • PARI
    is(n)=isprime(3^n-28) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(37)-a(42) from Robert Price, Dec 10 2013
Showing 1-10 of 15 results. Next

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