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Let p = prime(n); then a(n) = p + (p-1)/2.
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%I #13 Nov 04 2017 14:59:33

%S 4,7,10,16,19,25,28,34,43,46,55,61,64,70,79,88,91,100,106,109,118,124,

%T 133,145,151,154,160,163,169,190,196,205,208,223,226,235,244,250,259,

%U 268,271,286,289,295,298,316,334,340,343,349,358,361,376,385,394,403

%N Let p = prime(n); then a(n) = p + (p-1)/2.

%C Also numbers n such that (2n + 1)/3 is prime. - Vicente Izquierdo Gomez, Dec 30 2012

%F a(n) = (3*prime(n)-1)/2.

%e 3+2/2=4, 5+4/2=7, 7+6/2=10, 11+10/2=16,..

%t f[n_]:=n/2; lst={};Do[p=Prime[n];AppendTo[lst,p+f[p-1]],{n,2,5!}];lst

%t #+(#-1)/2&/@Prime[Range[2,60]] (* _Harvey P. Dale_, Nov 04 2017 *)

%Y Cf. A162939.

%K nonn

%O 2,1

%A _Vladimir Joseph Stephan Orlovsky_, Nov 30 2009

%E Edited by _N. J. A. Sloane_, Jan 04 2013