A217137 -id:A217137 - cp's OEIS frontend

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

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

Nicolas M. Perrault, Nov 10 2012

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

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

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.

Do[If[PrimeQ[3^n + 28], Print[n]], {n, 10000}]

is(n)=isprime(3^n+28) \\ Charles R Greathouse IV, Feb 17 2017

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

Nicolas M. Perrault, Nov 10 2012

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

			3^4 - 28 = 53 (prime), so 4 is in the sequence.

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.

Do[If[PrimeQ[3^n - 28], Print[n]], {n, 10000}]

is(n)=isprime(3^n-28) \\ Charles R Greathouse IV, Feb 17 2017

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

Nicolas M. Perrault, Nov 10 2012

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

			For k = 2, 3^2 + 32 = 41 (prime). Hence k = 2 is in the sequence.

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.

Do[If[PrimeQ[3^n + 32], Print[n]], {n, 10000}]

is(n)=isprime(3^n+32) \\ Charles R Greathouse IV, Feb 17 2017

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

Nicolas M. Perrault, Nov 10 2012

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

			3^5 - 32 = 211 (prime), so 5 is in the sequence.

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.

Do[If[PrimeQ[3^n - 32], Print[n]], {n, 10000}]

is(n)=isprime(3^n-32) \\ Charles R Greathouse IV, Feb 17 2017

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

Nicolas M. Perrault, Nov 10 2012

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

			For k = 2, 3^2 + 34 = 43 (prime), so 2 is in the sequence.

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.

Do[If[PrimeQ[3^n + 34], Print[n]], {n, 10000}]

is(n)=isprime(3^n+34) \\ Charles R Greathouse IV, Feb 17 2017

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

Nicolas M. Perrault, Nov 10 2012

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

			For k = 4, 3^4 - 34 = 47 and 47 is prime. Hence k = 4 is included in the sequence.

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.

Do[If[PrimeQ[3^n - 34], Print[n]], {n, 1, 10000}]
Select[Range[10000], PrimeQ[3^# - 34] &] (* Alonso del Arte, Nov 10 2012 *)

is(n)=isprime(3^n-34) \\ Charles R Greathouse IV, Feb 17 2017

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

A102907 Primes of the form 3^k + 10.

Original entry on oeis.org

11, 13, 19, 37, 739, 6571, 387420499, 150094635296999131, 57264168970223481226273458862846808078011946899, 2465034704958067503996131453373943813074726512397600979

Offset: 1

Roger L. Bagula, Mar 01 2005

nonn

Amiram Eldar, Table of n, a(n) for n = 1..16

Cf. A000040, A217137 (corresponding k's).

[a: n in [0..250] | IsPrime(a) where a is 3^n+10]; // Vincenzo Librandi, Nov 16 2010

a = Delete[Union[Flatten[Table[If [PrimeQ[3^n + 10] == True, 3^n + 10, 0], {n, 1, 200}]]], 1]

a(n) = 3^A217137(n) + 10. - Elmo R. Oliveira, Nov 11 2023

A217492 Numbers k such that 9^k + 10 is prime.

Original entry on oeis.org

0, 1, 3, 4, 9, 18, 49, 57, 67, 69, 106, 126, 258, 583, 1221, 1366, 4311, 11361, 12621, 14964, 16017, 22467, 25434, 45094, 51051, 89113

Offset: 1

Vincenzo Librandi, Oct 05 2012

Contains exactly the halved even terms of A217137.

Cf. A217137, A217347.

Select[Range[5000], PrimeQ[9^# + 10] &] (* Vincenzo Librandi, Oct 05 2012 *)

is(n)=ispseudoprime(9^n+10) \\ Charles R Greathouse IV, Jun 13 2017

a(18)-a(26) added from the data at A217137 by Amiram Eldar, Jun 19 2022

A217493 Numbers k such that 9^k - 10 is prime.

Original entry on oeis.org

2, 3, 4, 9, 11, 18, 19, 27, 28, 46, 50, 53, 80, 155, 203, 280, 451, 4963, 6167, 9687, 10083, 31450

Offset: 1

Vincenzo Librandi, Oct 05 2012

Contains exactly the halved even terms of A217347.

Cf. A217137, A217347.

Mathematica
```
Select[Range[5000], PrimeQ[9^# - 10] &]
```

is(n)=ispseudoprime(9^n-10) \\ Charles R Greathouse IV, Jun 13 2017

a(19)-a(22) added from the data at A217347 by Amiram Eldar, Jun 19 2022

A255542 a(n) = number of prime factors of (3^n + 10) counted with multiplicity.

Original entry on oeis.org

1, 1, 1, 1, 2, 2, 1, 3, 1, 2, 4, 3, 2, 3, 2, 3, 5, 3, 1, 3, 3, 3, 4, 2, 3, 4, 2, 6, 4, 3, 3, 4, 3, 2, 5, 4, 1, 4, 5, 5, 5, 2, 4, 3, 3, 5, 5, 2, 2, 5, 4, 3, 4, 3, 3, 6, 4, 4, 5, 5, 7, 3, 3, 4, 5, 5, 2, 6, 3, 5, 5, 4, 4, 5, 3, 7, 6, 4, 4, 3, 2, 4, 5, 4, 2, 4, 3, 2, 4, 4, 4, 5, 4, 6, 7, 4, 3, 5, 1, 4

Offset: 0

Zak Seidov, Feb 25 2015

nonn

			a(0) = 1 because 3^0+10 = 11 is prime.
a(4) = 2 because 3^4+10 = 91 = 7*13 is semiprime.
a(7) = 3 because 3^7+10 = 2197 = 13*13*13 is 3-almost prime.
a(10) = 4 because 3^7+10 = 59059 = 7*11*13*59 is 4-almost prime.
a(16) = 5 because 3^16+10 = 43046731 = 7*13*23*131*157 is 5-almost prime.

Amiram Eldar, Table of n, a(n) for n = 0..257 (terms 0..151 from Zak Seidov)

Cf. A001222, A102907, A217137.

Mathematica
```
a[n_]:= PrimeOmega[3^n+10];
```
PARI
```
a(n) = bigomega(3^n+10);
```

a(n) = A001222(3^n+10).

cp's OEIS Frontend

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

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

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

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

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

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

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A102907 Primes of the form 3^k + 10.

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A217492 Numbers k such that 9^k + 10 is prime.

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