A049496 -id:A049496 - cp's OEIS frontend

A049495 a(n) and a(n)+4^k are primes at least for k=1,2,3,4,5.

7, 37, 163, 9157, 9277, 15667, 53593, 56893, 111577, 135193, 137383, 142543, 305407, 467527, 470647, 476023, 480043, 527377, 607093, 671353, 761377, 817147, 885943, 891643, 904663, 1080073, 1116637, 1140847, 1172803, 1233523

Offset: 1

Labos Elemer

nonn

			7, 7+4=11, 7+16=23, 7+64=71, 7+256=263, 7+1024=1031 are all primes; the smallest such a sextuple is {7,11,23,71,263,1031}.

Michael De Vlieger, Table of n, a(n) for n = 1..1000

Cf. A023200, A049492-A049494, A049496-A049500.

Select[Prime@ Range[10^5], Function[p, AllTrue[Range@ 5, PrimeQ[p + 4^#] &]]] (* Michael De Vlieger, Aug 09 2017 *)

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

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

Original entry on oeis.org

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

Labos Elemer

nonn

			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}.

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

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

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

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

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

More terms from Michel Marcus, Dec 22 2013

cp's OEIS Frontend

A049495 a(n) and a(n)+4^k are primes at least for k=1,2,3,4,5.

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