A228026 Primes of the form 4^k + 3.

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

Offset

1,1

Links

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

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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).

Sequence in context: A305483 A046137 A193643 * A122484 A155242 A155333

Adjacent sequences: A228023 A228024 A228025 * A228027 A228028 A228029

Keyword

nonn,easy,changed

Author

Vincenzo Librandi, Aug 11 2013

Extensions

Cross-references corrected by Robert Price, Aug 01 2017

Status

approved