A049497 a(n) and a(n)+4^k are primes at least for k=1,2,3,4,5,6,7.

37, 163, 15667, 142543, 607093, 671353, 1457857, 2694157, 2979043, 4890307, 5772097, 6404773, 9139453, 10669003, 11170933, 11218747, 11905987, 13243063, 15130537, 18116473, 19433863, 21960577, 23524183, 25946083, 32380177, 45600157, 46960747, 51905137

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Examples

			37, 37+4=41, 37+16=53, 37+64=101, 37+256=293, 37+1024=1061, 37+4096=4133, 37+16384=16421 are all primes; the smallest such a 8-chain of primes is {37,41,53,101,293,1061,4133,16421}.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A023200, A049492-A049496, A049498-A049500.

Programs

Maple

filter:= n -> andmap(isprime, [n,n+4,n+4^2,n+4^3,n+4^4,n+4^5,n+4^6,n+4^7]):
select(filter, [seq(i,i=7..10^7,6)]); #Robert Israel, Nov 11 2019

PARI

isok(n) = isprime(n) && isprime(n+4) && isprime(n+16) && isprime(n+64) && isprime(n+256) && isprime(n+1024) && isprime(n+4096) && isprime(n+16384); \\ Michel Marcus, Dec 22 2013

Formula

A023200 INTERSECT A269859. - R. J. Mathar, Mar 26 2024

Extensions

More terms from Michel Marcus, Dec 22 2013