A157007 -id:A157007 - cp's OEIS frontend

A247952 Numbers k such that 2^k + 31 is prime.

4, 12, 36, 540, 844, 1192, 12136, 84280, 128356, 317464, 3018556

Offset: 1

Vincenzo Librandi, Sep 28 2014

Some terms correspond to probable primes. Lifchitz link shows Paul Underwood discovered 84280, and Lelio R Paula found 128356 and 317464 are in the sequence. - Jens Kruse Andersen, Sep 29 2014
a(11) > 5*10^5. - Robert Price, Oct 25 2015
All terms are even. - Elmo R. Oliveira, Nov 25 2023

Henri Lifchitz and Renaud Lifchitz, Search for 2^n+31, PRP Top Records.

Cf. A094076, A262971.

Cf. Numbers k such that 2^k + d is prime: (0,1,2,4,8,16) for d=1; A057732 (d=3), A059242 (d=5), A057195 (d=7), A057196 (d=9), A102633 (d=11), A102634 (d=13), A057197 (d=15), A057200 (d=17), A057221 (d=19), A057201 (d=21), A057203 (d=23), A157006 (d=25), A157007 (d=27), A156982 (d=29), this sequence (d=31), A247953 (d=33), A220077 (d=35).

Magma
```
[n: n in [0..2000]| IsPrime(2^n+31)];
```

Select[Range[0,10000], PrimeQ[2^# + 31] &]

is(n)=ispseudoprime(2^n+31) \\ Charles R Greathouse IV, May 22 2017

a(n) = 2*A262971(n). - Elmo R. Oliveira, Nov 25 2023

12136 and 84280 from Jens Kruse Andersen, Sep 29 2014
a(9)-a(10) (discovered by Lelio R Paula; see the Lifchitz link) added by Robert Price, Oct 04 2015
a(11) discovered by Robert Price, added by Elmo R. Oliveira, Nov 25 2023

A247953 Numbers k such that 2^k + 33 is prime.

Original entry on oeis.org

2, 3, 6, 11, 12, 14, 15, 20, 30, 60, 68, 75, 108, 116, 135, 206, 210, 410, 446, 558, 851, 1482, 1499, 2039, 2051, 4196, 7046, 7155, 8735, 10619, 18420, 20039, 46719, 75348, 179790, 203018, 434246

Offset: 1

Vincenzo Librandi, Sep 28 2014

Some terms correspond to probable primes. Lifchitz link shows the terms 179790 found by Donovan Johnson and 203018 by Lelio R Paula. - Jens Kruse Andersen, Sep 30 2014

a(38) > 5*10^5. - Robert Price, Nov 07 2015

Henri Lifchitz and Renaud Lifchitz, Search for 2^n+33, PRP Top Records.

Cf. A094076, A176926, A247957.

Cf. Numbers k such that 2^k + d is prime: (0,1,2,4,8,16) for d=1; A057732 (d=3), A059242 (d=5), A057195 (d=7), A057196 (d=9), A102633 (d=11), A102634 (d=13), A057197 (d=15), A057200 (d=17), A057221 (d=19), A057201 (d=21), A057203 (d=23), A157006 (d=25), A157007 (d=27), A156982 (d=29), A247952 (d=31), this sequence (d=33), A220077 (d=35).

/* The code gives only the terms up to 851: */ [n: n in [1..1400]| IsPrime( 2^n + 33 )];

A247957:=n->`if`(isprime(2^n+33),n,NULL): seq(A247957(n), n=0..1000); # Wesley Ivan Hurt, Sep 28 2014

Select[Range[10000], PrimeQ[2^# + 33] &]

is(n)=ispseudoprime(2^n+33) \\ Charles R Greathouse IV, Feb 20 2017

a(30)-a(34) from Jens Kruse Andersen, Sep 30 2014
a(35)-a(36) (discovered by Donovan Johnson and Lelio R Paula, respectively; see the Lifchitz link) added by Robert Price, Oct 04 2015
a(37) from Robert Price, Nov 07 2015

A156982 Numbers k such that 2^k + 29 is prime.

Original entry on oeis.org

1, 3, 5, 7, 9, 13, 15, 17, 23, 27, 33, 37, 43, 63, 69, 73, 79, 89, 117, 127, 239, 395, 409, 465, 837, 2543, 10465, 10837, 17005, 19285, 24749, 26473, 29879, 49197, 56673, 67119, 67689, 71007, 109393, 156403, 158757, 181913, 190945, 207865, 222943, 419637

Offset: 1

Edwin Dyke (ed.dyke(AT)btinternet.com), Feb 20 2009

nonn

n cannot be of the form 4m+2 or 4m because 2^(2m+2) + 29 is divisible by 3 and 2^4m + 29 is divisible by 15. - Avik Roy (avik_3.1416(AT)yahoo.co.in), Feb 21 2009

a(47) > 5*10^5. - Robert Price, Oct 25 2015

			For k = 1, 2^1 + 29 = 31.
For k = 3, 2^3 + 29 = 37.

Henri Lifchitz and Renaud Lifchitz, PRP Records, search for 2^n+29

Cf. A019434 (Fermat primes 2^(2^n)+1).

Cf. A057732, A059242, A057195, A057196, A102633, A102634, A057197, A057200, A057221, A057201, A057203, A157006, A157007, A247952, A247953, A220077.

[n: n in [0..1000] | IsPrime(2^n+29)]; // Vincenzo Librandi, Oct 05 2015

Delete[Union[Table[If[PrimeQ[2^n + 29], n, 0], {n, 1, 2600}]], 1]
Select[Range[500000], PrimeQ[2^#+29]&] (* Robert Price, Oct 04 2015 *)

is(n)=ispseudoprime(2^n+29) \\ Charles R Greathouse IV, Jun 06 2017

a(27)-a(38) from Robert Price, Oct 04 2015

a(39)-a(46) discovered by Henri Lifchitz from Lifchitz link by Robert Price, Oct 04 2015

A157006 Numbers k such that 2^k + 25 is prime.

Original entry on oeis.org

2, 4, 6, 8, 10, 20, 22, 34, 70, 92, 112, 118, 236, 250, 378, 438, 570, 654, 800, 1636, 2848, 4948, 5670, 6772, 7494, 8006, 9056, 11038, 16268, 21416, 21738, 33370, 78706, 112130, 126446, 164046, 219250, 236432, 368048, 524154, 530810, 640854, 699740, 746302, 754038, 754376, 931976, 989562

Offset: 1

Edwin Dyke (ed.dyke(AT)btinternet.com), Feb 20 2009

nonn

a(40) > 5*10^5. - Robert Price, Oct 15 2015

Since each term is even (n = 2*k), prime numbers of the form 2^k + 25 (see A104072) also have the form 4^k + 25. Those values of k are given in A204388. - Timothy L. Tiffin, Aug 06 2016

			For k = 2, 2^2 + 25 = 29.
For k = 4, 2^4 + 25 = 41.
For k = 6, 2^6 + 25 = 89.

Henri Lifchitz and Renaud Lifchitz, Search for 2^n+25, PRP Top Records.

Cf. A094076, A104072, A123250, A204388.

Cf. A019434 (primes 2^k+1), A057732 (2^k+3), A059242 (2^k+5), A057195 (2^k+7), A057196 (2^k+9), A102633 (2^k+11), A102634 (2^k+13), A057197 (2^k+15), A057200 (2^k+17), A057221 (2^k+19), A057201 (2^k+21), A057203 (2^k+23), this sequence (2^k+25), A157007 (2^k+27), A156982 (2^k+29), A247952 (2^k+31), A247953 (2^k+33), A220077 (2^k+35).

[n: n in [1..1000] | IsPrime(2^n+25)]; // Vincenzo Librandi, Aug 07 2016

Delete[Union[Table[If[PrimeQ[2^n + 25], n, 0], {n, 1, 1000}]], 1]
Select[Range[0, 10000], PrimeQ[2^# + 25] &] (* Vincenzo Librandi, Aug 07 2016 *)

is(n)=ispseudoprime(2^n+5^2) \\ Charles R Greathouse IV, Feb 20 2017

a(n) = 2*A204388(n). - Timothy L. Tiffin, Aug 09 2016

Extended by Vladimir Joseph Stephan Orlovsky, Feb 27 2011
a(29)-a(39) from Robert Price, Oct 15 2015
a(40)-a(48) found by Stefano Morozzi, added by Elmo R. Oliveira, Nov 25 2023

A220077 Numbers k such that 2^k + 35 is prime.

Original entry on oeis.org

1, 3, 5, 7, 9, 11, 15, 25, 33, 57, 117, 133, 189, 195, 263, 273, 287, 509, 693, 1087, 1145, 1159, 1845, 2743, 3275, 12223, 26263, 31425, 44359, 48003, 49251, 62557, 113877, 114507, 132865, 165789, 192549, 348437, 426043, 436365, 471043, 480417

Offset: 1

Vincenzo Librandi, Dec 04 2012

nonn

Some terms correspond to probable primes. Lifchitz link shows Lelio R Paula found the terms 132865, 165789, 192549, 348437. - Jens Kruse Andersen, Oct 01 2014
a(43) > 5*10^5. - Robert Price, Nov 01 2015
All terms are odd. - Elmo R. Oliveira, Nov 27 2023

Henri Lifchitz and Renaud Lifchitz, Search for 2^n+35, PRP Top Records.

Cf. A094076, A176927.

Cf. Numbers k such that 2^k + d is prime: (0,1,2,4,8,16) for d=1; A057732 (d=3), A059242 (d=5), A057195 (d=7), A057196 (d=9), A102633 (d=11), A102634 (d=13), A057197 (d=15), A057200 (d=17), A057221 (d=19), A057201 (d=21), A057203 (d=23), A157006 (d=25), A157007 (d=27), A156982 (d=29), A247952 (d=31), A247953 (d=33), this sequence (d=35).

Mathematica
```
Select[Range[5000],PrimeQ[2^# + 35] &]
```

for(n=1, 10^30, if (isprime(2^n + 35), print1(n", "))); \\ Altug Alkan, Oct 05 2015

a(26)-a(34) from Jens Kruse Andersen, Oct 01 2014
132865, 165789, 192549, 348437 discovered by Lelio R Paula confirmed as a(35)-a(38) by Robert Price, Oct 05 2015
a(39)-a(42) from Robert Price, Nov 01 2015

A104071 Primes of the form 2^k + 27.

Original entry on oeis.org

29, 31, 43, 59, 283, 1051, 8219, 16411, 65563, 1099511627803, 2199023255579, 17592186044443, 77371252455336267181195291, 1298074214633706907132624082305051

Offset: 1

Roger L. Bagula, Mar 02 2005

nonn

Cf. A000040, A157007.

[ a: n in [0..750] | IsPrime(a) where a is 2^n+27]; // Vincenzo Librandi, Nov 13 2010

a = Delete[Union[Flatten[Table[If [PrimeQ[2^n + 27] == True, 2^n + 27, 0], {n, 1, 400}]]], 1]

a(n) = 2^A157007(n) + 27. - Elmo R. Oliveira, Nov 08 2023

A262201 Prime p such that 2^p + 33 is also prime.

Original entry on oeis.org

2, 3, 11, 1499, 2039

Offset: 1

Robert Price, Oct 04 2015

a(6) > 203018.

A000040 INTERSECT A247953.

			For p=3, 2^3 + 33 = 41, which is prime.

Cf. A157007.

Cf. similar sequences of the type "Primes p such that 2^p + k" listed in A262098.

[p: p in PrimesUpTo(1000) | IsPrime(2^p+33)]; // Vincenzo Librandi, Oct 05 2015

Select[Prime[Range[100000]], PrimeQ[(2^# + 33)] &]

forprime(p=2, 10000, if (isprime(2^p + 33), print1(p", "))); \\ Altug Alkan, Oct 05 2015

A262934 Prime p such that 2^p + 27 is also prime.

Original entry on oeis.org

2, 5, 13, 41, 89113

Offset: 1

Robert Price, Oct 04 2015

a(6) > 376790.

			Prime 5 is in sequence because 2^5 + 27 = 59, which is also prime.

Cf. A157007.

Cf. similar sequences of the type "Primes p such that 2^p + k" listed in A262098.

[p: p in PrimesUpTo(100) | IsPrime(2^p+27)]; // Vincenzo Librandi, Oct 05 2015

Select[Prime[Range[100000]], PrimeQ[(2^# + 27)] &]

forprime(p=2, 10^30, if (isprime(2^p + 3^3), print1(p", "))); \\ Altug Alkan, Oct 04 2015

A000040 INTERSECT A157007.

A262969 Numbers k such that 4^k + 27 is prime.

Original entry on oeis.org

1, 2, 4, 5, 7, 8, 20, 22, 43, 55, 67, 77, 92, 97, 154, 160, 533, 748, 1432, 3143, 6427, 8257, 8270, 9623, 12269, 28822, 32683, 42638, 97427, 133340, 188395, 239044

Offset: 1

Robert Price, Oct 05 2015

The next terms are > 239044.

Contains exactly the halved even terms of A157007.

			For k = 22, 4^22 + 27 = 17592186044443 is prime.

Cf. A157007, A253772 (similar sequence).

[n: n in [0..700] | IsPrime(4^n+27)]; // Vincenzo Librandi, Oct 06 2015

Select[Range[0, 250000], PrimeQ[4^# + 27] &]

for(n=1, 1e3, if(isprime(4^n+3^3), print1(n", "))) \\ Altug Alkan, Oct 06 2015

a(32) derived from A157007 by Elmo R. Oliveira, Nov 28 2023

A172411 Numbers k such that 2^k+9 and 2^k+27 are prime.

Original entry on oeis.org

1, 2, 5, 10

Offset: 1

Juri-Stepan Gerasimov, Feb 02 2010

No further terms between 10 and 5000. - R. J. Mathar, Feb 07 2010

No further terms to 100000. Expected number of remaining terms: (zeta(2) - 1 - 1/4 - ... - 1/100000^2)/log^2 2 ~= 0.00002. - Charles R Greathouse IV, Mar 25 2010

			a(1)=1 because 2^1+3^2=11 and 2^1+3^3=29 are prime.

Select[Range[10],AllTrue[2^#+{9,27},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 28 2016 *)

is(n)=isprime(2^n+9) && isprime(2^n+27) \\ Charles R Greathouse IV, Sep 06 2016

A057196 INTERSECT A157007 - R. J. Mathar, Feb 07 2010

cp's OEIS Frontend

A247952 Numbers k such that 2^k + 31 is prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

Extensions

A247953 Numbers k such that 2^k + 33 is prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Extensions

A156982 Numbers k such that 2^k + 29 is prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Extensions

A157006 Numbers k such that 2^k + 25 is prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

Extensions

A220077 Numbers k such that 2^k + 35 is prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A104071 Primes of the form 2^k + 27.

Views

Author

Keywords

Crossrefs

Programs

Magma

Mathematica

Formula

A262201 Prime p such that 2^p + 33 is also prime.

Views

Author

Keywords

Comments

Examples