A179849 Sum of prime p and next prime after p is divisible by 7.

19, 41, 53, 103, 151, 211, 229, 263, 313, 397, 419, 439, 461, 479, 523, 557, 571, 709, 859, 881, 919, 977, 983, 991, 1033, 1049, 1069, 1091, 1103, 1109, 1117, 1171, 1187, 1193, 1279, 1301, 1327, 1427, 1447, 1453, 1489, 1499, 1571, 1621, 1709, 1721, 1747

Offset: 1

Author

Zak Seidov, Jan 10 2011

Keywords

• nonn

Comments

Also primes p such that the sum of p and next prime after p is a multiple of 14, since for p > 2 the sum of two consecutive primes is even. - Klaus Brockhaus, Jan 11 2011

Examples

			p=19, q=23, p+q=42=7*6=14*3; p=41, q=43, p+q=84=7*12=14*6.
		

Crossrefs

Cf. A031932 (lower prime of a difference of 14 between consecutive primes), A008596 (multiples of 14).

Programs

Magma

IsA179849:=func< n | IsPrime(n) and (n+NextPrime(n)) mod 14 eq 0 >; [ p: p in PrimesUpTo(2000) | IsA179849(p) ]; // Klaus Brockhaus, Jan 11 2011

Mathematica

fQ[n_] := Block[{q = NextPrime@ n}, Mod[n + q, 7] == 0]; Select[ Prime@ Range@ 300, fQ]

PARI

{q=3;for(n=1,100,p=q;q=nextprime(p+1);(p+q)%7==0&print(p))}