A141644 - OEIS

%I #5 Feb 01 2019 15:51:30

%S 3,19,41,173,181,281,347,373,401,409,433,449,461,461,479,499,509,541,

%T 547,571,577,619,691,701,709,859,881,919,929,1087,1091,1093,1097,1193,

%U 1229,1367,1367,1481,1483,1511,1523,1553,1559,1579,1601,1667,1697,1699

%N Primes of the form (p(2n)-p(n))/(7*2), where p(n)=n-th prime.

%e If n=10, then (p(10*2)-p(10))/7*2=(71-29)/14=3=a(1).

%e If n=45, then (p(45*2)-p(45))/7*2=(463-197)/14=19=a(2).

%e If n=85, then (p(85*2)-p(85))/7*2=(1013-439)/14=41=a(3).

%e If n=300, then (p(300*2)-p(300))/7*2=(4409-1987)/14=173=a(4).

%e If n=311, then (p(311*2)-p(311))/7*2=(4597-2063)/14=181=a(5).

%e If n=459, then (p(459*2)-p(459))/7*2=(7187-3253)/14=281=a(6), etc.

%t Select[Table[(Prime[2n]-Prime[n])/14,{n,3000}],PrimeQ] (* _Harvey P. Dale_, Feb 01 2019 *)

%Y Cf. A000040.

%Y Cf. A072473. [From _R. J. Mathar_, Oct 04 2008]

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Sep 18 2008

%E More terms from _R. J. Mathar_, Oct 04 2008

%E Definition clarified by _Harvey P. Dale_, Feb 01 2019