A217349 -id:A217349 - cp's OEIS frontend

A057195 Numbers k such that 2^k + 7 is prime.

2, 4, 6, 8, 10, 16, 18, 20, 28, 30, 38, 44, 78, 88, 98, 126, 160, 174, 204, 214, 588, 610, 798, 926, 1190, 1198, 1806, 1888, 2648, 3454, 3510, 3864, 3870, 8970, 12330, 13330, 18876, 22338, 39718, 55006, 110784, 172470, 196434, 235710, 247280, 268408, 279320, 300874, 315268, 372950, 472258, 566496, 780284, 820356

Offset: 1

Robert G. Wilson v, Sep 15 2000

nonn

Naturally all terms are even because (3-1)^(2n+1)+7 is divisible by 3. - Bruno Berselli, Oct 03 2012

Keith Conrad, Square patterns and infinitude of primes, University of Connecticut, 2019.
Jon Grantham and Andrew Granville, Fibonacci primes, primes of the form 2^n-k and beyond, arXiv:2307.07894 [math.NT], 2023.

Cf. A104066 (primes of the form 2^k+7).

A057195:=n->if isprime(2^n+7) then n; fi; seq(A057195(n), n=1..1000); # Wesley Ivan Hurt, Dec 06 2013

Do[ If[ PrimeQ[ 2^n +7 ], Print[n]], { n, 1, 15000 }]

is(n)=isprime(2^n+7) \\ Charles R Greathouse IV, Feb 17 2017

a(n) = 2*A217349(n). - Elmo R. Oliveira, Nov 12 2023

a(37)-a(51) from Robert Price, Dec 06 2013

a(51), a(53), a(54) from Jon Grantham, Jul 29 2023

A104066 Primes of the form 2^k + 7.

Original entry on oeis.org

11, 23, 71, 263, 1031, 65543, 262151, 1048583, 268435463, 1073741831, 274877906951, 17592186044423, 302231454903657293676551, 309485009821345068724781063, 316912650057057350374175801351

Offset: 1

Roger L. Bagula, Mar 02 2005

nonn

Also primes of the form 4^n+7 (in this case, the associated n are in A217349). - Bruno Berselli, Oct 03 2012

Cf. A000040, A057195 (numbers k such that 2^k + 7 is prime).

[a: n in [0..100 by 2] | IsPrime(a) where a is 2^n+7]; // Vincenzo Librandi, Jan 26 2011

a = Delete[Union[Flatten[Table[If [PrimeQ[2^n + 7] == True, 2^ n + 7, 0], {n, 1, 400}]]], 1]

list(lim)=my(v=List(),t); for(n=1,logint(lim\1-7,4), if(ispseudoprime(t=4^n+7), listput(v,t))); Vec(v) \\ Charles R Greathouse IV, Nov 17 2017

a(n) = 2^A057195(n) + 7. - Elmo R. Oliveira, Nov 08 2023

A253772 Numbers k such that 4^k + 13 is prime.

Original entry on oeis.org

1, 2, 4, 10, 19, 32, 40, 146, 566, 2054, 9967, 62639, 87814, 141092

Offset: 1

Vincenzo Librandi, Jan 12 2015

Numbers of the form 4^n+k (for n>0) are never primes when k is even (obviously) or when k == -1 (mod 6): in the last case, in fact, (3+1)^n + 6*h-1 is divisible by 3. - Bruno Berselli, Oct 06 2015

Cf. A104067.

Cf. Numbers k such that 4^k + d is prime: A089437 (d=3), A217349 (d=7), A217350 (d=9), this sequence (d=13), A253773 (d=15), A253774 (d=19), A262345 (d=21), A204388 (d=25), A262969 (d=27), A262971 (d=31), A262972 (d=33).

Magma
```
[n: n in [0..2000] | IsPrime(4^n+13)];
```
Mathematica
```
Select[Range[4000], PrimeQ[4^# + 13] &]
```

is(n)=ispseudoprime(4^n+13) \\ Charles R Greathouse IV, Feb 17 2017

a(n) = A102634(n)/2. - Elmo R. Oliveira, Nov 12 2023

a(11)-a(14) derived from A102634 by Robert Price, Sep 06 2015

cp's OEIS Frontend

A057195 Numbers k such that 2^k + 7 is prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

Extensions

A104066 Primes of the form 2^k + 7.

Views

Author

Keywords

Comments

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

A253772 Numbers k such that 4^k + 13 is prime.

Views

Author

Keywords

Comments

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

Extensions