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Numbers n such that both n and n+1 are composite numbers that sum up to a Pythagorean prime (i.e., of the form 4k+1).
10

%I #10 Jul 26 2015 03:55:25

%S 8,14,20,26,44,48,50,54,56,68,74,86,90,98,114,116,120,128,134,140,146,

%T 158,168,174,176,186,194,200,204,216,224,230,254,260,278,284,288,296,

%U 300,308,320,326,338,350,354,380,384,386,398,404,410,414,426,428,440

%N Numbers n such that both n and n+1 are composite numbers that sum up to a Pythagorean prime (i.e., of the form 4k+1).

%F Equals (A096785 - 1)/2.

%t Select[ Range[450], PrimeQ[ # ] == PrimeQ[ # + 1] == PrimeQ[2# + 1, GaussianIntegers -> True] == 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=465;n=4;while(n<m,k=nextcomposite(n+1);p=n+k;if(k==n+1&&isprime(p)&&p%4==1,print1(n,","));n=k)} \\ _Klaus Brockhaus_, Jul 11 2004

%Y Subsequence (even numbers) of A096784. See A096785 for the associated primes.

%Y Cf. A060254, A096784, A096785, A096787, A096788, A096675.

%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