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%I #11 Sep 08 2022 08:45:14
%S 8,9,14,15,20,21,26,33,35,39,44,48,50,51,54,56,63,65,68,69,74,75,81,
%T 86,90,95,98,99,105,111,114,116,119,120,125,128,134,135,140,141,146,
%U 153,155,158,165,168,174,176,183,186,189,194,200,204,209,215,216,219,221
%N Numbers n such that both n and n+1 are composite numbers that sum up to a prime.
%F Equals (A060254 -1)/2.
%t Select[ Range[ 225], PrimeQ[ # ] == PrimeQ[ # + 1] == False && PrimeQ[2# + 1] == True &] (* _Robert G. Wilson v_, Jul 11 2004 *)
%o (PARI) nextcomposite(k)=if(k<3,4,if(isprime(k),k+1,k));
%o {m=230;n=4;while(n<m,k=nextcomposite(n+1);p=n+k;if(k==n+1&&isprime(p),print1(n,","));n=k)} \\ _Klaus Brockhaus_, Jul 11 2004
%o (Magma)[n: n in [0..250]|not IsPrime(n) and not IsPrime(n+1) and IsPrime(2*n+1)] // _Vincenzo Librandi_, Dec 18 2010
%Y See A060254 for the primes 2n+1.
%Y Cf. A096785, A096786, A096787, A096788.
%K nonn
%O 1,1
%A _Lekraj Beedassy_, Jul 09 2004
%E Corrected and extended by _Klaus Brockhaus_ and _Ray Chandler_, Jul 10 2004
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