%I #17 Apr 08 2024 06:55:52

%S 17,29,41,53,89,97,101,109,113,137,149,173,181,197,229,233,241,257,

%T 269,281,293,317,337,349,353,373,389,401,409,433,449,461,509,521,557,

%U 569,577,593,601,617,641,653,677,701,709,761,769,773,797,809,821,829,853

%N Primes of form 4k+1 which are the sum of two consecutive composite numbers.

%F Equals 1 + 2*A096786.

%t Do[If[PrimeQ[2*n+1]&&Equal[Mod[s, 4], 1]&&!PrimeQ[n]&&!PrimeQ[n+1], Print[2*n+1]], {n, 1, 1000}] (* _Labos Elemer_ *)

%t 2Select[ Range[450], PrimeQ[ # ] == PrimeQ[ # + 1] == PrimeQ[2# + 1, GaussianIntegers -> True] == False && PrimeQ[2# + 1] == True &] + 1 (* _Robert G. Wilson v_, Jul 11 2004 *)

%o (PARI) nextcomposite(k)=if(k<3,4,if(isprime(k),k+1,k));

%o {m=440;n=4;while(n<m,k=nextcomposite(n+1);p=n+k;if(k==n+1&&isprime(p)&&p%4==1,print1(p,","));n=k)} \\ _Klaus Brockhaus_, Jul 11 2004

%Y Subsequence of A060254. See A096786 for values 2n. See A096675 for n values.

%Y Cf. A060254, A096784, A096786, A096787, A096788, A096675, A096678.

%K nonn

%O 1,1

%A _Lekraj Beedassy_, Jul 09 2004

%E Corrected and extended by _Klaus Brockhaus_, _Rick L. Shepherd_ and _Ray Chandler_, Jul 10 2004