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a(n) = Sum_{k=1..n} 2^prime(k).
9

%I #21 Jul 17 2022 08:02:30

%S 0,4,12,44,172,2220,10412,141484,665772,9054380,545925292,2693408940,

%T 140132362412,2339155617964,11135248640172,151872736995500,

%U 9159071991736492,585619824295159980,2891462833508853932,150465415423185266860,2511648656858007873708

%N a(n) = Sum_{k=1..n} 2^prime(k).

%C a(468) has 1000 decimal digits. - _Michael De Vlieger_, Jul 14 2017

%H Michael De Vlieger, <a href="/A076793/b076793.txt">Table of n, a(n) for n = 0..467</a>

%F a(n) = a(n-1) + 2^prime(n).

%e a(1) = 2^prime(1) = 2^2 = 4; a(2) = 4 + 2^prime(2) = 4 + 2^3 = 12.

%t Table[Sum[2^Prime[k], {k, n}], {n, 0, 18}] (* _Michael De Vlieger_, Jul 14 2017 *)

%o (PARI) a(n) = sum(k=1, n, 2^prime(k)) \\ _Michel Marcus_, Jul 23 2013

%Y Cf. A000040, A076794.

%Y Partial sums of A034785.

%K easy,nonn

%O 0,2

%A _Walter Carlini_, Nov 17 2002

%E More terms from _R. J. Mathar_, Aug 31 2007