login
Product of two consecutive primes divided by the next prime and rounded down.
1

%I #15 Jun 28 2017 23:38:31

%S 1,2,3,5,8,11,14,15,21,24,27,35,37,38,42,51,53,57,65,65,69,73,76,85,

%T 95,97,101,103,96,109,121,129,127,137,143,145,153,157,161,171,169,179,

%U 187,191,185,188,207,221,223,223,231,229,235,245,251,261,263,267,275

%N Product of two consecutive primes divided by the next prime and rounded down.

%H G. C. Greubel, <a href="/A185371/b185371.txt">Table of n, a(n) for n = 2..1000</a>

%F a(n)=[p(n)*p(n+1)/p(n+2)], where p(n) is the n-th prime and [] is the floor function .

%F For n > 3, prime(n)/2 < a(n) < prime(n). prime(n) - a(n) << log(n)^2 under Cramer's conjecture. Weaker estimates follow from the Prime Number Theorem. - _Charles R Greathouse IV_, Jan 26 2012

%e [2*3/5]=1; [3*5/7]=2; [5*7/11]=3

%t Table[Floor[Prime[n]*Prime[n + 1]/Prime[n + 2]], {n, 1, 50}] (* _G. C. Greubel_, Jun 28 2017 *)

%o (PARI) p=2;q=3;forprime(r=5,1e3,print1(p*q\r", ");p=q;q=r) \\ _Charles R Greathouse IV_, Jan 26 2012

%K nonn

%O 2,2

%A Tyler Carrico, Jan 26 2012

%E a(14)-a(15) corrected, a(16)-a(59) from _Charles R Greathouse IV_, Jan 26 2012