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a(n) = (1/4)*Sum_{j=1..n} 2^prime(j).
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%I #32 Mar 20 2022 17:34:13

%S 0,1,3,11,43,555,2603,35371,166443,2263595,136481323,673352235,

%T 35033090603,584788904491,2783812160043,37968184248875,

%U 2289767997934123,146404956073789995,722865708377213483,37616353855796316715,627912164214501968427,2989095405649324575275

%N a(n) = (1/4)*Sum_{j=1..n} 2^prime(j).

%H G. C. Greubel, <a href="/A135482/b135482.txt">Table of n, a(n) for n = 0..450</a> (a(0) = 0 added by _M. F. Hasler_).

%F a(n) = A076793(n)/4. - _M. F. Hasler_, Oct 30 2018

%p A135482:= n-> add(2^ithprime(i)/4, i=1..n): seq(A135482(n), n=0..20); # _Wesley Ivan Hurt_, Feb 02 2014

%t Accumulate[Table[Floor[2^i/4],{i,Prime[Range[20]]}]] (* _Harvey P. Dale_, Dec 05 2013 *)

%o (Magma) [&+[2^(NthPrime(k)-2): k in [1..n]]: n in [1..25]]; // _Bruno Berselli_, Sep 24 2015

%o (PARI) a(n) = sum(k=1, n, 2^prime(k))/4; \\ _Michel Marcus_, Oct 15 2016

%Y Cf. A000040, A000079, A076793, A080355.

%Y Partial sums of A135620.

%K nonn

%O 0,3

%A _Ctibor O. Zizka_, Feb 07 2008

%E More terms from _Harvey P. Dale_, Dec 05 2013

%E a(0) = 0 prepended by _M. F. Hasler_, Oct 30 2018