A057733 -id:A057733 - cp's OEIS frontend

A228032 Primes of the form 8^n + 3.

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

A023568 Number of distinct prime divisors of prime(n)-3.

Original entry on oeis.org

0, 0, 1, 1, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 1, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 3, 2, 2, 2, 3, 3, 2, 3, 3, 2, 2, 2, 2, 2, 3, 2, 3, 3, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 3, 3, 3

Offset: 1

Clark Kimberling

nonn

a(n) = 1 if prime(n) is in A057733. - Robert Israel, Dec 28 2015

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A023569, A057733.

0,0,seq(nops(numtheory:-factorset(ithprime(i)-3)), i=3..100); # Robert Israel, Dec 28 2015

Join[{0,0},PrimeNu/@(Prime[Range[3,100]]-3)] (* Harvey P. Dale, Sep 09 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

A228033 Primes of the form 8^k + 5.

Original entry on oeis.org

13, 2787593149816327892691964784081045188247557, 15177100720513508366558296147058741458143803430094840009779784451085189728165691397

Offset: 1

Vincenzo Librandi, Aug 11 2013

a(4) = 8^64655 + 5 = 1.919...*10^58389 is too large to include. - Amiram Eldar, Jul 23 2025

Cf. A217355 (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=5), 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 [1..300] | IsPrime(a) where a is 8^n+5];

Select[Table[8^n + 5, {n, 4000}], PrimeQ]

A023569 Greatest prime divisor of prime(n) - 3.

Original entry on oeis.org

2, 2, 2, 5, 7, 2, 5, 13, 7, 17, 19, 5, 11, 5, 7, 29, 2, 17, 7, 19, 5, 43, 47, 7, 5, 13, 53, 11, 31, 2, 67, 17, 73, 37, 11, 5, 41, 17, 11, 89, 47, 19, 97, 7, 13, 11, 7, 113, 23, 59, 17, 31, 127, 13, 19, 67, 137, 139, 7, 29, 19, 11, 31, 157, 41, 167, 43, 173, 7, 89

Offset: 3

Clark Kimberling

nonn

a(n) = 2 if prime(n) is in A057733. - Robert Israel, Dec 28 2015

Robert Israel, Table of n, a(n) for n = 3..10000

Cf. A023568, A057733.

seq(max(numtheory:-factorset(ithprime(i)-3)), i=3..100); # Robert Israel, Dec 28 2015

Table[FactorInteger[Prime[n] - 3] [[-1, 1]], {n, 3, 100}] (* Vincenzo Librandi, Dec 29 2015 *)

a(n) = vecmax(factor(prime(n)-3)[,1]); \\ Michel Marcus, Dec 29 2015

Corrected by Robert Israel, Dec 29 2015

A156973 Primes of the form 2^k + 17.

Original entry on oeis.org

19, 8209, 2097169, 8589934609, 2417851639229258349412369, 680564733841876926926749214863536422929, 62165404551223330269422781018352605012557018849668464680057997111644937126566671941649

Offset: 1

Edwin Dyke (ed.dyke(AT)btinternet.com), Feb 19 2009

nonn

			19 = 2^1 + 17 is in the sequence;
8209 = 2^13 + 17 is in the sequence.

Cf. A000040, A057200, A057733 (2^k + 3), A123250 (2^k + 5), A104066 (2^k + 7), A156940 (2^k + 11), A104067 (2^k + 13).

[ a: n in [1..400] | IsPrime(a) where a is 2^n+17 ]; // Vincenzo Librandi, Nov 27 2010

Delete[Union[Table[If[PrimeQ[2^n + 17], 2^n + 17, 0], {n, 1, 300}]],1]

a(n) = 2^A057200(n) + 17. - Elmo R. Oliveira, Nov 08 2023

a(7) from Vincenzo Librandi, Apr 29 2010

cp's OEIS Frontend

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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A228030 Primes of the form 7^n + 6.

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A228031 Primes of the form 7^n + 10.

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A023568 Number of distinct prime divisors of prime(n)-3.

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A228027 Primes of the form 4^k + 9.

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A228033 Primes of the form 8^k + 5.

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