%I
%S 11,23,47,83,131,191,263,397,563,709,953,1091,1289,1531,1867,2129,
%T 2389,2729,2963,3259,3659,4099,4787,5387,5693,6101,6473,6803,7829,
%U 8999,9697,10247,11117,12041,12703,13669,14549,15439,16573,17321,18461,19661
%N Primes of the form [prime(n)*prime(n+1)+p]/2 with increasing p.
%C Also primes equal to the arithmetic mean between product of two consecutive primes and prime p.
%H Vincenzo Librandi, <a href="/A100558/b100558.txt">Table of n, a(n) for n = 1..1000</a>
%e a(2)=11 because 11=(3*5+7)/2 and p is 7;
%e a(3)=23 because 23=(5*7+11)/2 and p is 11;
%e a(4)=47 because 47=(7*11+17)/2 and p is 17;
%e a(5)=83 because 83=(11*13+23)/2 and p is 23.
%t a[2] = 11; a[n_] := a[n] = Block[{k = PrimePi[2a[n  1]  Prime[n  1]Prime[n]] + 1, q = Prime[n]Prime[n + 1]}, While[p = Prime[k]; !PrimeQ[(q + p)/2], k++ ]; (q + p)/2]; Table[ a[n], {n, 2, 43}] (* _Robert G. Wilson v_, Nov 29 2004 *)
%K nonn
%O 1,1
%A _Giovanni Teofilatto_, Nov 28 2004
%E Edited and extended by _Robert G. Wilson v_, Nov 29 2004
