A158714 Primes p such that p1 = ceiling(p/2) + p is prime and p2 = floor(p1/2) + p1 is prime.
3, 19, 67, 307, 379, 467, 547, 587, 739, 859, 1259, 1699, 1747, 1867, 2027, 2699, 2819, 3259, 3539, 4019, 4507, 5059, 5779, 7547, 8219, 8539, 8747, 8819, 9547, 10067, 10499, 10667, 11939, 13259, 13627, 13859, 14939, 17659, 17707, 17987, 18859
Offset: 1
Keywords
Examples
67 is in the sequence because 67, ceiling(67/2) + 67 = 101 and floor(101/2) + 101 = 151 are all primes.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Maple
N:= 10^5; # to get all entries <= N filter:= proc(p) local p1,p2; if not isprime(p) then return false fi; p1:= ceil(p/2)+p; if not isprime(p1) then return false fi; p2:= floor(p1/2)+p1; isprime(p2); end proc; select(filter,[seq(2*i+1,i=1..floor((N-1)/2)]; # Robert Israel, May 09 2014 -
Mathematica
lst={};Do[p=Prime[n];If[PrimeQ[p=Ceiling[p/2]+p],If[PrimeQ[p=Floor[p/2]+p],AppendTo[lst,Prime[n]]]],{n,7!}];lst
Extensions
Definition corrected by Robert Israel, May 09 2014
Comments