A226502 - OEIS

%I #11 Jun 10 2013 21:42:50

%S 11,34,36,96,60,144,160,162,360,198,320,336,352,494,460,720,378,560,

%T 718,450,972,1020,938,1002,816,420,864,1752,960,2596,810,2204,576,

%U 2404,1220,1606,1980,1694,1420,2876,744,2694,780,3160,2810,3520,3170,1824,1840,1422,3836

%N Let P(k) denote the k-th prime (P(1)=2, P(2)=3 ...); a(n) = P(n+1)P(n+3) - P(n)P(n+2).

%C Differences of the products of alternate primes.

%F a(n) >> n log n and this is probably sharp: on Dickson's conjecture there are infinitely many a(n) < kn log n for any k > 4. The constant 4 comes from 8 + 2 - 6 - 0 n the prime quadruplet (p+0, p+2, p+6, p+8). On Cramér's conjecture a(n) = O(n log^3 n). Unconditionally a(n) << n^1.525 log n. - _Charles R Greathouse IV_, Jun 10 2013

%o (PARI) p=2;q=3;r=5;forprime(s=7,1e2,print1(q*s-p*r", ");p=q;q=r;r=s) \\ _Charles R Greathouse IV_, Jun 10 2013

%Y First differences of A090076.

%K nonn,easy

%O 1,1

%A _Ed Smiley_, Jun 09 2013