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

1,1

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

Links

Table of n, a(n) for n=1..47.

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A356471 A019393 A378121 * A029489 A155024 A323391

Adjacent sequences: A179846 A179847 A179848 * A179850 A179851 A179852

Keyword

nonn

Author

Zak Seidov, Jan 10 2011

Status

approved