A123250 -id:A123250 - 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

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

A156940 Primes of the form 2^k + 11.

Original entry on oeis.org

13, 19, 43, 139, 523, 32779, 8388619, 536870923, 2147483659, 36028797018963979, 2361183241434822606859, 151115727451828646838283, 254629497041810760783555711051172270131433549208242031329517556169297662470417088272924683

Offset: 1

Edwin Dyke (ed.dyke(AT)btinternet.com), Feb 18 2009

nonn

Cf. A057733, A123250, A104066.

[ a: n in [0..350] | IsPrime(a) where a is 2^n+11 ]; // Vincenzo Librandi, Nov 26 2010

Delete[Union[Table[If[PrimeQ[2^n + 11], 2^n + 11, 0], {n, 1, 200}]],1]

a(n) = 2^A102633(n) + 11. - R. J. Mathar, Feb 20 2009

a(13) from Vincenzo Librandi, Apr 29 2010

A228026 Primes of the form 4^k + 3.

Original entry on oeis.org

7, 19, 67, 4099, 65539, 262147, 268435459, 1073741827, 19342813113834066795298819

Offset: 1

Vincenzo Librandi, Aug 11 2013

			67 is a term because 4^3 + 3 = 67 is prime.

Vincenzo Librandi, Table of n, a(n) for n = 1..16

Cf. A089437 (associated k).

Cf. Primes of the form r^k + h: A092506 (r=2, h=1), A057733 (r=2, h=3), A123250 (r=2, h=5), A104066 (r=2, h=7), A104070 (r=2, h=9), A057735 (r=3, h=2), A102903 (r=3, h=4), A102870 (r=3, h=8), A102907 (r=3, h=10), A290200 (r=4, h=1), this sequence (r=4, h=3), A228027 (r=4, h=9), A182330 (r=5, h=2), A228029 (r=5, h=6), A102910 (r=5, h=8), A182331 (r=6, h=1), A104118 (r=6, h=5), A104115 (r=6, h=7), A104065 (r=7, h=4), A228030 (r=7, h=6), A228031 (r=7, h=10), A228032 (r=8, h=3), A228033 (r=8, h=5), A144360 (r=8, h=7), A145440 (r=8, h=9), A228034 (r=9, h=2), A159352 (r=10, h=3), A159031 (r=10, h=7).

[a: n in [0..200] | IsPrime(a) where a is  4^n+3];

Select[Table[4^n + 3, {n, 0, 200}], PrimeQ]

a(n) = 4^A089437(n) + 3. - Elmo R. Oliveira, Nov 14 2023

Cross-references corrected by Robert Price, Aug 01 2017

A228032 Primes of the form 8^n + 3.

Original entry on oeis.org

11, 67, 4099, 32771, 262147, 1073741827, 19342813113834066795298819

Offset: 1

Vincenzo Librandi, Aug 11 2013

Vincenzo Librandi, Table of n, a(n) for n = 1..14

Cf. A217354 (associated n).

Cf. Primes of the form k^n + h: A092506 (k=2, h=1), A057733 (k=2, h=3), A123250 (k=2, h=5), A104066 (k=2, h=7), A104070 (k=2, h=9), A057735 (k=3, h=2), A102903 (k=3, h=4), A102870 (k=3, h=8), A102907 (k=3, h=10), A290200 (k=4, h=1), A182330 (k=5, h=2), A102910 (k=5, h=8), A182331 (k=6, h=1), A104118 (k=6, h=5), A104115 (k=6, h=7), A104065 (k=7, h=4), this sequence (k=8, h=3), A144360 (k=8, h=7), A145440 (k=8, h=9), A228034 (k=9, h=2), A159352 (k=10, h=3), A159031 (k=10, h=7).

[a: n in [0..300] | IsPrime(a) where a is  8^n+3];

Select[Table[8^n + 3, {n, 0, 300}], PrimeQ]

Corrected cross-references - Robert Price, Aug 01 2017

A243429 Primes of the form 2^n + 39.

Original entry on oeis.org

41, 43, 47, 71, 103, 167, 1063, 2087, 8231, 131111, 536870951, 8589934631, 549755813927, 8796093022247, 154742504910672534362390567, 40564819207303340847894502572071, 162259276829213363391578010288167, 2722258935367507707706996859454145691687

Offset: 1

Vincenzo Librandi, Jun 05 2014

nonn

Associated n: 1, 2, 3, 5, 6, 7, 10, 11, 13, 17, 29, 33, 39, 43, 87, 105, 107, 131, 253, 329, ....

Vincenzo Librandi, Table of n, a(n) for n = 1..34

Cf. primes of the form 2^n+k: A092506 (k=1), A057733 (k=3), A123250 (k=5), A104066 (k=7), A104070 (k=9), A156940 (k=11), A104067 (k=13), A144487 (k=15), A156973 (k=17), A104068 (k=19), A156983 (k=21), A176922 (k=23), A104072 (k=25), A104071 (k=27), A156974 (k=29), A104069 (k=31), A176926 (k=33), A176927 (k=35), A176924 (k=37), this sequence (k=39), A176925 (k=41), A243430 (k=43), A243431 (k=45), A243432 (k=47), A104073 (k=49).

[a: n in [0..500] | IsPrime(a) where a is 2^n+39];

Select[Table[2^n + 39, {n, 0, 500}], PrimeQ]

A228029 Primes of the form 5^n + 6.

Original entry on oeis.org

7, 11, 31, 131, 631, 1220703131

Offset: 1

Vincenzo Librandi, Aug 11 2013

Vincenzo Librandi, Table of n, a(n) for n = 1..15

Cf. A089142 (associated n).

Cf. Primes of the form k^n + h: A092506 (k=2, h=1), A057733 (k=2, h=3), A123250 (k=2, h=5), A104066 (k=2, h=7), A104070 (k=2, h=9), A057735 (k=3, h=2), A102903 (k=3, h=4), A102870 (k=3, h=8), A102907 (k=3, h=10), A290200 (k=4, h=1), A182330 (k=5, h=2), this sequence (k=5, h=6), A102910 (k=5, h=8), A182331 (k=6, h=1), A104118 (k=6, h=5), A104115 (k=6, h=7), A104065 (k=7, h=4), A144360 (k=8, h=7), A145440 (k=8, h=9), A228034 (k=9, h=2), A159352 (k=10, h=3), A159031 (k=10, h=7).

[a: n in [0..200] | IsPrime(a) where a is  5^n+6];

Select[Table[5^n + 6, {n, 0, 200}], PrimeQ]

Corrected cross-references - Robert Price, Aug 01 2017

A228030 Primes of the form 7^n + 6.

Original entry on oeis.org

7, 13, 349, 33232930569607, 2651730845859653471779023381607

Offset: 1

Vincenzo Librandi, Aug 11 2013

Vincenzo Librandi, Table of n, a(n) for n = 1..7

Cf. A217130 (associated n).

Cf. Primes of the form k^n + h: A092506 (k=2, h=1), A057733 (k=2, h=3), A123250 (k=2, h=5), A104066 (k=2, h=7), A104070 (k=2, h=9), A057735 (k=3, h=2), A102903 (k=3, h=4), A102870 (k=3, h=8), A102907 (k=3, h=10), A290200 (k=4, h=1), A182330 (k=5, h=2), A102910 (k=5, h=8), A182331 (k=6, h=1), A104118 (k=6, h=5), A104115 (k=6, h=7), A104065 (k=7, h=4), this sequence (k=7, h=6), A144360 (k=8, h=7), A145440 (k=8, h=9), A228034 (k=9, h=2), A159352 (k=10, h=3), A159031 (k=10, h=7).

[a: n in [0..300] | IsPrime(a) where a is  7^n+6];

Select[Table[7^n + 6, {n, 0, 300}], PrimeQ]

Corrected cross-references - Robert Price, Aug 01 2017

A228031 Primes of the form 7^n + 10.

Original entry on oeis.org

11, 17, 59, 353, 2411, 117659, 823553, 1977326753, 9387480337647754305659, 3219905755813179726837617, 44567640326363195900190045974568017, 616873509628062366290756156815389726793178417, 30226801971775055948247051683954096612865741953

Offset: 1

Vincenzo Librandi, Aug 11 2013

Vincenzo Librandi, Table of n, a(n) for n = 1..21

Cf. A217132 (associated n).

Cf. Primes of the form k^n + h: A092506 (k=2, h=1), A057733 (k=2, h=3), A123250 (k=2, h=5), A104066 (k=2, h=7), A104070 (k=2, h=9), A057735 (k=3, h=2), A102903 (k=3, h=4), A102870 (k=3, h=8), A102907 (k=3, h=10), A290200 (k=4, h=1), A182330 (k=5, h=2), A102910 (k=5, h=8), A182331 (k=6, h=1), A104118 (k=6, h=5), A104115 (k=6, h=7), A104065 (k=7, h=4), this sequence (k=7, h=10), A144360 (k=8, h=7), A145440 (k=8, h=9), A228034 (k=9, h=2), A159352 (k=10, h=3), A159031 (k=10, h=7).

[a: n in [0..300] | IsPrime(a) where a is  7^n+10];

Select[Table[7^n + 10, {n, 0, 300}], PrimeQ]

Corrected cross-references - Robert Price, Aug 01 2017

A228027 Primes of the form 4^k + 9.

Original entry on oeis.org

13, 73, 1033, 262153, 1073741833, 73786976294838206473, 4835703278458516698824713

Offset: 1

Vincenzo Librandi, Aug 11 2013

Subsequence of A104070. - Elmo R. Oliveira, Nov 28 2023

			262153 is a term because 4^9 + 9 = 262153 is prime.

Vincenzo Librandi, Table of n, a(n) for n = 1..12

Cf. A000040, A217350 (corresponding k's).

Cf. Primes of the form r^k + h: A092506 (r=2, h=1), A057733 (r=2, h=3), A123250 (r=2, h=5), A104066 (r=2, h=7), A104070 (r=2, h=9), A057735 (r=3, h=2), A102903 (r=3, h=4), A102870 (r=3, h=8), A102907 (r=3, h=10), A290200 (r=4, h=1), A228026 (r=4, h=3), this sequence (r=4, h=9), A182330 (r=5, h=2), A228029 (r=5, h=6), A102910 (r=5, h=8), A182331 (r=6, h=1), A104118 (r=6, h=5), A104115 (r=6, h=7), A104065 (r=7, h=4), A228030 (r=7, h=6), A228031 (r=7, h=10), A228032 (r=8, h=3), A228033 (r=8, h=5), A144360 (r=8, h=7), A145440 (r=8, h=9), A228034 (r=9, h=2), A159352 (r=10, h=3), A159031 (r=10, h=7).

[a: n in [0..200] | IsPrime(a) where a is 4^n+9];

Select[Table[4^n + 9, {n, 0, 200}],PrimeQ]

a(n) = 4^A217350(n) + 9. - Elmo R. Oliveira, Nov 28 2023

Corrected cross-references - Robert Price, Aug 01 2017

cp's OEIS Frontend

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

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

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A156940 Primes of the form 2^k + 11.

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A228026 Primes of the form 4^k + 3.

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A228032 Primes of the form 8^n + 3.

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A243429 Primes of the form 2^n + 39.

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A228029 Primes of the form 5^n + 6.

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