login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A269259 Primes p such that p+2^4, p+2^6, p+2^8, p+2^10 and p+2^12 are all primes. 6

%I

%S 37,163,15667,22093,40177,47287,53593,114577,120607,142543,234067,

%T 242377,255907,263047,263803,305407,388117,444607,460387,503287,

%U 527143,607093,671353,784897,904663,938947,1063903,1086493,1172803,1216807,1233523,1288543

%N Primes p such that p+2^4, p+2^6, p+2^8, p+2^10 and p+2^12 are all primes.

%H Dana Jacobsen, <a href="/A269259/b269259.txt">Table of n, a(n) for n = 1..10476</a>

%e The prime 37 is in the sequence, since 37 + 16 = 53, 37 + 64 = 101, 37 + 256 = 293, 37 + 1024 = 1061 and 37 + 4096 = 4133 are all primes.

%e The prime 163 is in the sequence, since 163 + 16 = 179, 163 + 64 = 227, 163 + 256 = 419, 163 + 1024 = 1187 and 163 + 4096 = 4259 are all primes.

%t m = {2^4, 2^6, 2^8, 2^10, 2^12}; Select[Prime@ Range[2*10^5], Times @@ Boole@ PrimeQ[# + m] == 1 &] (* _Michael De Vlieger_, Jul 13 2016 *)

%o (PARI) is(n) = for(k=2, 6, if(!ispseudoprime(2^(2*k)+n), return(0))); return(1)

%o forprime(p=1, 16e5, if(is(p), print1(p, ", "))) \\ _Felix Fröhlich_, Jul 12 2016

%o (Perl) use ntheory ":all"; say for sieve_prime_cluster(2,1e6, 16,64,256,1024,4096); # _Dana Jacobsen_, Jul 13 2016

%o (MAGMA) [p: p in PrimesInInterval(2,1600000) | forall{i: i in [16,64,256,1024,4096] | IsPrime(p+i)}]; // _Vincenzo Librandi_, Jul 16 2016

%Y Subsequence of A269258.

%Y Cf. A269257.

%K nonn

%O 1,1

%A _Debapriyay Mukhopadhyay_, Jul 12 2016

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 20 14:54 EST 2019. Contains 329337 sequences. (Running on oeis4.)