A247953 -id:A247953 - cp's OEIS frontend

A157007 Numbers k such that 2^k + 27 is prime.

1, 2, 4, 5, 8, 10, 13, 14, 16, 40, 41, 44, 86, 110, 125, 133, 134, 145, 154, 184, 194, 301, 308, 320, 685, 1001, 1066, 1496, 1633, 2005, 2864, 3241, 6286, 11585, 12854, 16514, 16540, 19246, 24538, 28705, 57644, 65366, 85276, 89113, 194854, 266680, 376790, 478088

Offset: 1

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

nonn

a(49) > 5*10^5. - Robert Price, Nov 06 2015

			For k = 1, 2^1 + 27 = 29.
For k = 2, 2^2 + 27 = 31.
For k = 4, 2^4 + 27 = 43.

Henri Lifchitz and Renaud Lifchitz, Search for 2^n+27, PRP Top Records.

Cf. A057733, A094076, A104071, A123250.

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), A157006 (2^k+25), this sequence (2^k+27), A156982 (2^k+29), A247952 (2^k+31), A247953 (2^k+33), A220077 (2^k+35).

[n: n in [0..1000] | IsPrime(2^n+27)]; // Vincenzo Librandi, Oct 05 2015

Delete[Union[Table[If[PrimeQ[2^n + 27], n, 0], {n, 1, 2000}]], 1]
Select[Range[5000],PrimeQ[2^#+27]&] (* Harvey P. Dale, Mar 24 2011 *)

for(n=1, 1e3, if(isprime(2^n+3^3), print1(n", "))) \\ Altug Alkan, Oct 04 2015

More terms from Harvey P. Dale, Mar 24 2011
a(33)-a(42) from Robert Price, Oct 04 2015
a(43)-a(47) discovered by Henri Lifchitz and Lelio R Paula from Lifchitz link by Robert Price, Oct 04 2015
a(48) from Robert Price, Nov 06 2015

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

Original entry on oeis.org

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

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

A176926 Primes of the form 2^k + 33.

Original entry on oeis.org

37, 41, 97, 2081, 4129, 16417, 32801, 1048609, 1073741857, 1152921504606847009, 295147905179352825889, 37778931862957161709601, 324518553658426726783156020576289, 83076749736557242056487941267521569

Offset: 1

Vincenzo Librandi, Apr 29 2010

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..25

Cf. A000040, A247953 (corresponding k's).

[ a: n in [0..750] | IsPrime(a) where a is 2^n+33 ]

Select[Table[2^n + 33, {n, 300}], PrimeQ] (* Vincenzo Librandi Dec 01 2012 *)

a(n) = 2^A247953(n) + 33. - 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

A262972 Numbers k such that 4^k + 33 is prime.

Original entry on oeis.org

1, 3, 6, 7, 10, 15, 30, 34, 54, 58, 103, 105, 205, 223, 279, 741, 2098, 3523, 9210, 37674, 89895, 101509, 217123

Offset: 1

Robert Price, Oct 05 2015

Contains exactly the halved even terms of A247953.

The next terms are > 2*10^5.

			For k = 30, 4^30 + 33 = 1152921504606847009 is prime.

Cf. A247953, A253772 (similar sequence).

[n: n in [0..700] | IsPrime(4^n+33)]; // Vincenzo Librandi, Oct 06 2015

Select[Range[0, 250000], PrimeQ[4^# + 33] &]

for(n=1, 1e3, if(isprime(4^n+33), print1(n", "))) \\ Altug Alkan, Oct 06 2015

a(23) derived from A247953 by Elmo R. Oliveira, Nov 28 2023

cp's OEIS Frontend

A157007 Numbers k such that 2^k + 27 is prime.

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

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

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

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

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A176926 Primes of the form 2^k + 33.

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

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