A057913 -id:A057913 - cp's OEIS frontend

A211486 Primes of the form 5+3*2^k.

11, 17, 29, 53, 101, 197, 389, 773, 49157, 196613, 1572869, 12582917, 50331653, 402653189, 1610612741, 12884901893, 824633720837, 54043195528445957, 432345564227567621, 3458764513820540933, 226673591177742970257413, 59421121885698253195157962757

Offset: 1

Vincenzo Librandi, Apr 13 2012

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..40

Cf. A057913 (n such that 3*2^n + 5 is prime).

Cf. A057197, A144487.

[ a: n in [0..250] | IsPrime(a) where a is 5+3*2^n ];

Mathematica
```
Select[5+2^Range[0,2000]*3,PrimeQ]
```

{for(n=0, 80, if(isprime(k=5+3*2^n), print1(k, ", ")))}

A057912 Numbers k such that 3*2^k - 5 is prime.

Original entry on oeis.org

2, 3, 4, 7, 9, 10, 13, 15, 25, 31, 34, 48, 52, 64, 109, 145, 162, 204, 207, 231, 271, 348, 444, 553, 559, 1504, 1708, 3048, 3970, 4423, 4668, 5737, 5877, 6130, 8584, 10663, 12517, 16591, 18450, 19362, 22291, 34468, 36637, 52212, 59040, 130279, 236511, 392260, 496411, 536868, 565024, 662703, 908005

Offset: 1

Robert G. Wilson v, Nov 16 2000

a(44) > 44233. - Jinyuan Wang, Feb 02 2020

a(54) > 1000000 - Jon Grantham, Jul 30 2023

Jon Grantham and Andrew Granville, Fibonacci primes, primes of the form 2^n-k and beyond, arXiv:2307.07894 [math.NT], 2023.

Cf. A057913 (3*2^k + 5 is prime).

Cf. A048488 (3*2^k - 5, but with different offset).

Do[ If[ PrimeQ[ 3*2^n - 5 ], Print[ n ] ], {n, 1, 3000} ]

is(n)=ispseudoprime(3*2^n-5) \\ Charles R Greathouse IV, Jun 13 2017

a(36)-a(41) from Vincenzo Librandi, Oct 10 2013
a(42)-a(43) from Jinyuan Wang, Feb 02 2020
a(44)-a(45) from Michael S. Branicky, May 20 2023
a(46)-a(53) from Jon Grantham, Jul 30 2023

A212317 Numbers m such that both 32^m + 5 and 52^m + 3 are prime.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 8, 32

Offset: 1

Zak Seidov, Oct 24 2013

No more terms?

Intersection of A057913 and A058586.

Select[Range[0,2200], PrimeQ[5*2^#+3] && PrimeQ[3*2^#+5]&]

A227230 Numbers k such that 3*2^k + {5,7} are twin primes.

Original entry on oeis.org

1, 2, 3, 5, 6, 19, 22

Offset: 1

Zak Seidov, Sep 20 2013

No more terms up to 10^4.
Any subsequent terms exceed 200,000. - Lucas A. Brown, Sep 02 2024
Any subsequent terms exceed 10^6, by non-primality of 3*2^k+7 for members of b-file at A057913 > 22 and table in Section 6 of Grantham and Granville link. - Michael S. Branicky, Sep 07 2024

Jon Grantham and Andrew Granville, Fibonacci primes, primes of the form 2^n-k and beyond, arXiv:2307.07894 [math.NT], 2023.

Intersection of A057913 and A059746. - Jason Yuen, Sep 02 2024

Cf. A071558, A181490.

Reap[Do[If[PrimeQ[a=3*2^n+5]&&PrimeQ[a+2],Sow[n]],{n,150}]][[2,1]]

for(k = 1,10^4, if(ispseudoprime(a = 3*2^k + 5)&&ispseudoprime (a + 2), print1(k",")))

cp's OEIS Frontend

A211486 Primes of the form 5+3*2^k.

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A057912 Numbers k such that 3*2^k - 5 is prime.

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Extensions

A212317 Numbers m such that both 32^m + 5 and 52^m + 3 are prime.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

A227230 Numbers k such that 3*2^k + {5,7} are twin primes.

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Author

Keywords

Comments

Links

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Programs

Mathematica

PARI

cp's OEIS Frontend

A211486 Primes of the form 5+3*2^k.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

A057912 Numbers k such that 3*2^k - 5 is prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A212317 Numbers m such that both 3*2^m + 5 and 5*2^m + 3 are prime.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

A227230 Numbers k such that 3*2^k + {5,7} are twin primes.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

A212317 Numbers m such that both 32^m + 5 and 52^m + 3 are prime.