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 A158714 Primes p such that p1 = ceiling(p/2) + p is prime and p2 = floor(p1/2) + p1 is prime. 7

%I

%S 3,19,67,307,379,467,547,587,739,859,1259,1699,1747,1867,2027,2699,

%T 2819,3259,3539,4019,4507,5059,5779,7547,8219,8539,8747,8819,9547,

%U 10067,10499,10667,11939,13259,13627,13859,14939,17659,17707,17987,18859

%N Primes p such that p1 = ceiling(p/2) + p is prime and p2 = floor(p1/2) + p1 is prime.

%C All a(n) == 3 (mod 8), as this is necessary for p, p1 and p2 to be odd. - _Robert Israel_, May 11 2014

%H Robert Israel, <a href="/A158714/b158714.txt">Table of n, a(n) for n = 1..10000</a>

%e 67 is in the sequence because 67, ceiling(67/2) + 67 = 101 and floor(101/2) + 101 = 151 are all primes.

%p N:= 10^5; # to get all entries <= N

%p filter:= proc(p)

%p local p1,p2;

%p if not isprime(p) then return false fi;

%p p1:= ceil(p/2)+p;

%p if not isprime(p1) then return false fi;

%p p2:= floor(p1/2)+p1;

%p isprime(p2);

%p end proc;

%p select(filter,[seq(2*i+1,i=1..floor((N-1)/2)]; # _Robert Israel_, May 09 2014

%t 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

%Y Cf. A158708, A158709, A158710, A158711, A158712, A158713, A242366.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Mar 24 2009

%E Definition corrected by _Robert Israel_, May 09 2014

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Last modified July 26 13:40 EDT 2021. Contains 346294 sequences. (Running on oeis4.)