A157006 -id:A157006 - 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

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

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

A104072 Primes of the form 2^n + 5^2.

Original entry on oeis.org

29, 41, 89, 281, 1049, 1048601, 4194329, 17179869209, 1180591620717411303449, 4951760157141521099596496921, 5192296858534827628530496329220121, 332306998946228968225951765070086169

Offset: 1

Roger L. Bagula, Mar 02 2005

nonn

Primes of the form 4^n + 4! + 1. - Vincenzo Librandi, Nov 13 2010
Indeed, calculating mod 3 we have 2^n + 5^2 = (-1)^n + 1 = 0 if n is odd, so n must be even to yield a prime. - M. F. Hasler, Nov 13 2010
Those even values of n are given in A157006.  Since n = 2k, these prime numbers also have the form 4^k + 25, where k is given in A204388. - Timothy L. Tiffin, Aug 06 2016
These primes a(m) can be used to generate numbers having deficiency 26. The formula a(m)*(a(m)-25)/2 produces those terms in A275702 having rightmost digit 8. - Timothy L. Tiffin, Aug 09 2016

			From _Timothy L. Tiffin_, Aug 07 2016: (Start)
a(1) = 2^2  + 5^2 =       4 + 25 =      29.
a(2) = 2^4  + 5^2 =      16 + 25 =      41.
a(3) = 2^6  + 5^2 =      64 + 25 =      89.
a(4) = 2^8  + 5^2 =     256 + 25 =     281.
a(5) = 2^10 + 5^2 =    1024 + 25 =    1049.
a(6) = 2^20 + 5^2 = 1048576 + 25 = 1048601. (End)

Cf. A157006, A204388, A275702.

a = Delete[Union[Flatten[Table[If [PrimeQ[2^n + 25] == True, 2^n + 25, 0], {n, 1, 400}]]], 1]
Select[2^Range[0,120]+25,PrimeQ] (* Harvey P. Dale, Jun 20 2017 *)

a(m) = 2^(A157006(m)) + 5^2 = 4^(A204388(m)) + 25. - Timothy L. Tiffin, Aug 07 2016

If n == 0 mod 4, then a(m) == 1 mod 10. If n == 2 mod 4, then a(m) == 9 mod 10. - Timothy L. Tiffin, Aug 09 2016

A204388 Numbers k such that 4^k + 25 is prime.

Original entry on oeis.org

1, 2, 3, 4, 5, 10, 11, 17, 35, 46, 56, 59, 118, 125, 189, 219, 285, 327, 400, 818, 1424, 2474, 2835, 3386, 3747, 4003, 4528, 5519, 8134, 10708, 10869, 16685, 39353, 56065, 63223, 82023, 109625, 118216, 184024, 262077, 265405, 320427, 349870, 373151, 377019, 377188, 465988, 494781

Offset: 1

Juri-Stepan Gerasimov, Jan 15 2012

nonn

a(40) > 2.5*10^5. - Robert Price, Oct 17 2015

Since 4^(6k) + 25 = 4096^k + 25 == (1^k + 25) mod 13 = 26 mod 13 == 0 mod 13, no multiple of 6 will be in this sequence. - Timothy L. Tiffin, Aug 07 2016

			From _Timothy L. Tiffin_, Aug 09 2016: (Start)
 a(1) = 1, since 4^1 + 25 = 4 + 25 = 29, which is prime.
 a(2) = 2, since 4^2 + 25 = 16 + 25 = 41, which is prime.
 a(3) = 3, since 4^3 + 25 = 64 + 25 = 89, which is prime.
 a(4) = 4, since 4^4 + 25 = 256 + 25 = 281, which is prime.
 a(5) = 5, since 4^5 + 25 = 1024 + 25 = 1049, which is prime.
 a(6) = 10, since 4^10 + 25 = 1048576 + 25 = 1048601, which is prime. (End)

Cf. A057196, A104072, A157006.

[n: n in [1..1000] | IsPrime(4^n+25)]; // Vincenzo Librandi, Aug 07 2016

Select[Range[2000], PrimeQ[4^# + 25] &] (* T. D. Noe, Feb 03 2012 *)

for(n=1, 1e5, if(isprime(4^n + 25), print1(n", "))) \\ Altug Alkan, Oct 17 2015

a(n) = A157006(n)/2. - Robert Price, Oct 17 2015

a(22)-a(39) derived from A157006 by Robert Price, Oct 17 2015

a(40)-a(48) derived from A157006 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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A247953 Numbers k such that 2^k + 33 is prime.

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

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Magma

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

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A104072 Primes of the form 2^n + 5^2.

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A204388 Numbers k such that 4^k + 25 is prime.

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