A162714 -id:A162714 - cp's OEIS frontend

A363024 Primes of the form 3^(k-1) - 2^k.

11, 179, 601, 1931, 10456158899, 617669101316651, 984770866999239144049, 2153693958571958138940251, 1570042898793851235488822819, 14130386090585813000157964091, 11972515182561981102976512358583456508049, 19088056323407826758511836230558252318494847619

Offset: 1

Sébastien Tao, May 13 2023

nonn

a(23) has 1117 digits. - Michael S. Branicky, May 26 2023

			a(1) = 3^3 - 2^4 = 27 - 16 = 11 (prime).
a(2) = 3^5 - 2^6 = 243 - 64 = 179 (prime).

Michael S. Branicky, Table of n, a(n) for n = 1..22

Prime terms in A003063.

Cf. A162714, A363375, A162715 (subsequence).

Select[Table[3^(k - 1) - 2^k, {k, 1 , 100}], PrimeQ]

A162715 Primes of the form 3^p-2^(p+1), where p is also a prime.

Original entry on oeis.org

11, 179, 1931, 617669101316651, 14130386090585813000157964091, 19088056323407826758511836230558252318494847619

Offset: 1

Vincenzo Librandi, Jul 11 2009

nonn

The next term has 1117 digits and is not included explicitly for that reason.

Cf. A162714.

[a: p in PrimesInInterval(3,1200) | IsPrime(a) where a is 3^p - 2^(p + 1)]; // Vincenzo Librandi, Sep 11 2013

Select[Table[3^p - 2^(p + 1), {p, Prime[Range[70]]}], PrimeQ] (* Vincenzo Librandi, Sep 11 2013 *)

a(n) = 3^A162714(n)-2^(1+A162714(n)) .

Clarified status of p in the definition - R. J. Mathar, Oct 16 2009

A363375 Numbers k such that 3^(k-1) - 2^k is prime.

Original entry on oeis.org

4, 6, 7, 8, 22, 32, 45, 52, 58, 60, 85, 98, 211, 290, 291, 426, 428, 712, 903, 1392, 1683, 1828, 2342, 3482, 4818, 4887, 9060, 14328, 16948, 17581, 18358, 65298, 69237, 84770, 94788

Offset: 1

Sébastien Tao, May 29 2023

a(36) > 100000. - Hugo Pfoertner, Jun 03 2023

			a(1) = 4 is in the sequence because 3^3 - 2^4 =  11 is prime.
a(2) = 6 is in the sequence because 3^5 - 2^6 = 179 is prime.

Cf. A057468, A162714, A363024.

The sequence that results from increasing all terms by 1 in A162714 is a subsequence.

Cases[Range[1, 300], k_ /; PrimeQ[3^(k - 1) - 2^k]]

a(16)-a(31) from Michael S. Branicky, May 29 2023
a(32)-a(33) from Hugo Pfoertner, May 29 2023
a(34)-a(35) from Hugo Pfoertner, Jun 02 2023

cp's OEIS Frontend

A363024 Primes of the form 3^(k-1) - 2^k.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A162715 Primes of the form 3^p-2^(p+1), where p is also a prime.

Views

Author

Keywords

Comments

Crossrefs

Programs

Magma

Mathematica

Formula

Extensions

A363375 Numbers k such that 3^(k-1) - 2^k is prime.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

Extensions