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%I #12 Apr 12 2017 04:43:19
%S 2,5,17,77,381,1851,8893,41741,191755,868151,3875933,17120309,
%T 74950547,325590115,1405167561,6029676711,25750781177,109495928099,
%U 463852117169,1958476902435,8244703036797,34615624751259,144991244981985
%N Sum of the first 2^n primes.
%H Robert G. Wilson v, <a href="/A099825/b099825.txt">Table of n, a(n) for n = 0..30</a>
%H C. Hilliard, <a href="http://groups.msn.com/First300billionprimes/sumprimeslt2n.msnw">Sumprimes</a>.
%t NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; f[0] = 2; f[n_] := f[n] = Block[{k = 0, mx = 2^n/2, np = Prime[2^n/2], s = f[n - 1]}, While[k < mx, k++; np = NextPrim@np; s = s + np]; s]; Table[ f@n, {n, 0, 23)] (* _Robert G. Wilson v_ Aug 24 2006 *)
%t Module[{nn=22,ap},ap=Accumulate[Prime[Range[2^nn]]];Table[ap[[2^n]],{n,0,nn}]] (* _Harvey P. Dale_, Apr 12 2017 *)
%o (PARI) a(n)=my(s); forprime(p=2,, s+=p; if(n--==0, return(s))) \\ _Charles R Greathouse IV_, Feb 16 2017
%Y Cf. A000040, A006988, A007504, A099824, A099826, A121248.
%K nonn
%O 0,1
%A _Robert G. Wilson v_, Oct 25 2004
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