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.

Previous Showing 11-16 of 16 results.

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

A219048 Numbers k such that 3^k + 32 is prime.

Original entry on oeis.org

2, 3, 4, 6, 23, 24, 38, 164, 172, 176, 207, 216, 251, 272, 424, 1112, 1318, 2072, 2664, 3143, 4704, 5236, 9526, 13064, 13523, 27111, 35931, 37504, 47542, 128656, 181551
Offset: 1

Views

Author

Nicolas M. Perrault, Nov 10 2012

Keywords

Comments

a(32) > 2*10^5. - Robert Price, Nov 15 2013

Examples

			For k = 2, 3^2 + 32 = 41 (prime). Hence k = 2 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 + 32], Print[n]], {n, 10000}]
  • PARI
    is(n)=isprime(3^n+32) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(23)-a(31) from Robert Price, Nov 15 2013

A219049 Numbers k such that 3^k - 32 is prime.

Original entry on oeis.org

5, 8, 18, 21, 69, 84, 181, 216, 461, 642, 672, 2413, 3681, 5666, 12281, 14949, 19508, 27817, 34061, 43236, 43733, 81828
Offset: 1

Views

Author

Nicolas M. Perrault, Nov 10 2012

Keywords

Comments

a(23) > 2*10^5. - Robert Price, Dec 22 2013

Examples

			3^5 - 32 = 211 (prime), so 5 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 - 32], Print[n]], {n, 10000}]
  • PARI
    is(n)=isprime(3^n-32) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(15)-a(22) from Robert Price, Dec 22 2013

A219050 Numbers k such that 3^k + 34 is prime.

Original entry on oeis.org

1, 2, 3, 5, 7, 9, 10, 17, 27, 34, 51, 57, 61, 89, 98, 171, 547, 569, 769, 874, 1105, 2198, 2307, 3937, 4685, 5105, 5582, 11131, 11821, 15902, 24626, 36401, 46195, 50974, 65198, 66685
Offset: 1

Views

Author

Nicolas M. Perrault, Nov 10 2012

Keywords

Comments

a(37) > 2*10^5. - Robert Price, Nov 24 2013

Examples

			For k = 2, 3^2 + 34 = 43 (prime), so 2 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 + 34], Print[n]], {n, 10000}]
  • PARI
    is(n)=isprime(3^n+34) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(28)-a(36) from Robert Price, Nov 24 2013

A219051 Numbers k such that 3^k - 34 is prime.

Original entry on oeis.org

4, 7, 11, 13, 29, 32, 36, 44, 79, 157, 197, 341, 467, 996, 1421, 2479, 3269, 5203, 7987, 9341, 14836, 26047, 47816, 64304, 100693, 127597, 167167, 174697, 182089, 198791
Offset: 1

Views

Author

Nicolas M. Perrault, Nov 10 2012

Keywords

Comments

a(31) > 2*10^5. - Robert Price, Nov 23 2013

Examples

			For k = 4, 3^4 - 34 = 47 and 47 is prime. Hence k = 4 is included 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 - 34], Print[n]], {n, 1, 10000}]
Select[Range[10000], PrimeQ[3^# - 34] &] (* Alonso del Arte, Nov 10 2012 *)
  • PARI
    is(n)=isprime(3^n-34) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(21)-a(30) from Robert Price, Nov 23 2013

A102904 Primes of the form 3^k + 20.

Original entry on oeis.org

23, 29, 47, 101, 263, 2207, 6581, 59069, 177167, 4782989, 984770902183611232901, 174449211009120179071170527, 278128389443693511257285776231781, 7509466514979724803946715958257567
Offset: 1

Views

Author

Roger L. Bagula, Mar 01 2005

Keywords

Comments

The sequence of the corresponding k starts 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, ... [Joerg Arndt, Jul 19 2012]

Links

Crossrefs

Cf. A000040, A000960, A219040 (corresponding k's).

Programs

  • Magma
    [ a: n in [0..100] | IsPrime(a) where a is 3^n+20 ]; // Vincenzo Librandi, Jul 19 2012
  • Mathematica
    Select[Table[3^n+20, {n,0,200}],PrimeQ] (* Vincenzo Librandi, Jul 19 2012 *)

Formula

a(n) = 3^A219040(n) + 20. - Elmo R. Oliveira, Nov 12 2023
Previous Showing 11-16 of 16 results.

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