A104066 -id:A104066 - 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

A168415 a(n) = 2^n + 7.

Original entry on oeis.org

8, 9, 11, 15, 23, 39, 71, 135, 263, 519, 1031, 2055, 4103, 8199, 16391, 32775, 65543, 131079, 262151, 524295, 1048583, 2097159, 4194311, 8388615, 16777223, 33554439, 67108871, 134217735, 268435463, 536870919, 1073741831, 2147483655

Offset: 0

Vincenzo Librandi, Dec 01 2009

a(n) is prime <=> a(n) is in A104066 <=> n is in A057195 <=> 2^(n-1)*a(n) = A257272(n) is in A125247. - M. F. Hasler, Apr 27 2015

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-2).

Cf. A000079, A057195, A104066, A125247, A257272.

[2^n+7: n in [0..40]]; // Vincenzo Librandi, Sep 19 2013

a[n_]:=2^n+7; a[Range[0,200]] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2011*)
CoefficientList[Series[(8 - 15 x)/((2 x - 1) (x - 1)), {x, 0, 200}], x] (* Vincenzo Librandi, Sep 19 2013 *)
LinearRecurrence[{3,-2},{8,9},40] (* Harvey P. Dale, Mar 03 2014 *)

a(n)=1<Charles R Greathouse IV, Sep 20 2011

a(n) = 2*a(n-1) - 7, n > 1.
G.f.: (8 - 15*x)/((2*x - 1)*(x - 1)). - R. J. Mathar, Jul 10 2011
a(n) = A000079(n) + 7. - Omar E. Pol, Sep 20 2011
E.g.f.: exp(2*x) + 7*exp(x). - G. C. Greubel, Jul 22 2016
a(n) = 3*a(n-1) - 2*a(n-2) for n > 1. - Elmo R. Oliveira, Nov 11 2023

A144242 Prime numbers of the form 8^k +- 7.

Original entry on oeis.org

71, 262151, 1073741831, 549755813881, 302231454903657293676551, 85070591730234615865843651857942052871, 23945242826029513411849172299223580994042798784118791, 25711008708143844408671393477458601640355247900524685364822023

Offset: 1

Reikku Kulon, Sep 15 2008

nonn

Amiram Eldar, Table of n, a(n) for n = 1..14

Cf. A000040, A000668, A104066, A144231, A144232, A144233, A144234, A144236.

Select[Sort[Flatten[Table[8^k+{7,-7},{k,90}]]],PrimeQ] (* Harvey P. Dale, Aug 08 2016 *)

a(8) from Amiram Eldar, Jul 24 2025

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

cp's OEIS Frontend

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

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A168415 a(n) = 2^n + 7.

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A144242 Prime numbers of the form 8^k +- 7.

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A156940 Primes of the form 2^k + 11.

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Magma

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A228026 Primes of the form 4^k + 3.

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Magma

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A228032 Primes of the form 8^n + 3.

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Magma

Mathematica

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A243429 Primes of the form 2^n + 39.

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Magma

Mathematica

A228029 Primes of the form 5^n + 6.

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