A228027 Primes of the form 4^k + 9.

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

Offset: 1

Author

Vincenzo Librandi, Aug 11 2013

Keywords

• nonn
• easy

Comments

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

Examples

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

Links

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

Crossrefs

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).

Programs

Magma

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

Mathematica

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

Formula

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

Extensions

Corrected cross-references - Robert Price, Aug 01 2017