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A309152 Numbers that can be written as the sum of two primes whose difference is also prime. 6

%I

%S 7,8,9,12,15,21,24,33,36,45,60,63,75,84,105,111,120,141,144,153,183,

%T 195,201,204,216,231,243,273,276,285,300,315,351,360,384,396,423,435,

%U 456,465,480,525,540,564,573,603,621,624,645,663,696,813,825,831,840

%N Numbers that can be written as the sum of two primes whose difference is also prime.

%C Numbers k such that k = p + q where p < q and p, q, and q - p are all prime.

%C Union of A054735 and (A006512 + 2). - _Robert Israel_, Jul 15 2019

%C From _Bernard Schott_, Jul 15 2019: (Start)

%C If k is even, then k is in A054735 with q - p = 2.

%C If k is odd, then k is in (A006512 + 2) with p = 2. (End)

%H Robert Israel, <a href="/A309152/b309152.txt">Table of n, a(n) for n = 1..10000</a>

%p P:= select(isprime, {seq(i,i=3..10000,2)}):

%p T:= P intersect map(`+`,P,2):

%p A1:= map(`+`,T, 2):

%p A2:= select(`<`, map(t -> 2*t-2, T), max(A1)):

%p sort(convert(A1 union A2,list); # _Robert Israel_, Jul 15 2019

%o (PARI) is(n) = my(x=n-1, y=1); while(x >= y, if(ispseudoprime(x) && ispseudoprime(y), if(ispseudoprime(x-y), return(1))); x--; y++); 0 \\ _Felix Fröhlich_, Jul 14 2019

%Y Cf. A006512, A054735.

%K nonn

%O 1,1

%A _Wesley Ivan Hurt_, Jul 14 2019

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Last modified July 29 15:44 EDT 2021. Contains 346346 sequences. (Running on oeis4.)