A174519 - OEIS

%I #5 Nov 21 2013 12:50:00

%S 14,25,56,70,98,112,140,264,243,297,396,280,308,528,689,513,567,726,

%T 490,675,858,924,1350,1235,700,728,742,770,2242,2318,1452,1215,1859,

%U 1885,1377,2041,1782,1848,2249,1593,2405,2431,1358,1372,3060,5275,3723,1582

%N Sum of 3 consecutive primes and of all composite numbers in-between.

%C 2+3+4+5=14, 3+4+5+6+7=25, 5+6+7+8+9+10+11=56, ..

%t f[n_,x_]:=n*x+x*(x+1)/2;Table[Prime[n]+f[Prime[n],Prime[n+2]-Prime[n]-1]+Prime[n+2],{n,5!}]

%t sm[{a_,b_,c_}]:=(c-a+1) (a+c)/2; sm/@Partition[Prime[Range[50]],3,1] (* _Harvey P. Dale_, Mar 11 2012 *)

%Y Cf. A034962, A054265, A174518

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Mar 21 2010