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

7, 8, 9, 12, 15, 21, 24, 33, 36, 45, 60, 63, 75, 84, 105, 111, 120, 141, 144, 153, 183, 195, 201, 204, 216, 231, 243, 273, 276, 285, 300, 315, 351, 360, 384, 396, 423, 435, 456, 465, 480, 525, 540, 564, 573, 603, 621, 624, 645, 663, 696, 813, 825, 831, 840

Offset: 1

Author

Wesley Ivan Hurt, Jul 14 2019

Keywords

• nonn

Comments

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

Union of A054735 and (A006512 + 2). - Robert Israel, Jul 15 2019

From Bernard Schott, Jul 15 2019: (Start)

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

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006512, A054735.

Programs

Maple

P:= select(isprime, {seq(i,i=3..10000,2)}):
T:= P intersect map(`+`,P,2):
A1:= map(`+`,T, 2):
A2:= select(`<`, map(t -> 2*t-2, T), max(A1)):
sort(convert(A1 union A2,list); # Robert Israel, Jul 15 2019

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