This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A099825 #30 Aug 05 2025 13:35:50
%S A099825 2,5,17,77,381,1851,8893,41741,191755,868151,3875933,17120309,
%T A099825 74950547,325590115,1405167561,6029676711,25750781177,109495928099,
%U A099825 463852117169,1958476902435,8244703036797,34615624751259,144991244981985,605994279458465,2527803622205465
%N A099825 Sum of the first 2^n primes.
%H A099825 Amiram Eldar, <a href="/A099825/b099825.txt">Table of n, a(n) for n = 0..65</a> (calculated using Kim Walisch's primesum program; terms 0..30 from Robert G. Wilson v)
%H A099825 Cino Hilliard, <a href="http://groups.msn.com/First300billionprimes/sumprimeslt2n.msnw">Sumprimes</a>. [broken link]
%H A099825 Kim Walisch, <a href="https://github.com/kimwalisch/primesum">Sum of the primes below x (primesum)</a>.
%F A099825 a(n) = A007504(A000079(n)). - _Amiram Eldar_, Jul 01 2024
%t A099825 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 A099825 Module[{nn=22,ap},ap=Accumulate[Prime[Range[2^nn]]];Table[ap[[2^n]],{n,0,nn}]] (* _Harvey P. Dale_, Apr 12 2017 *)
%o A099825 (PARI) a(n)=my(s); n=2^n; forprime(p=2,, s+=p; if(n--==0, return(s))) \\ _Charles R Greathouse IV_, Feb 16 2017 \\ corrected by _David A. Corneth_, Aug 05 2025
%Y A099825 Cf. A000040, A000079, A006988, A007504, A033844, A099824, A099826, A121248.
%K A099825 nonn
%O A099825 0,1
%A A099825 _Robert G. Wilson v_, Oct 25 2004