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A144043 a(2n-1) = 2*prime(n), a(2n) = prime(n) + prime(n+1).

%I A144043 #31 Nov 02 2023 23:41:46
%S A144043 4,5,6,8,10,12,14,18,22,24,26,30,34,36,38,42,46,52,58,60,62,68,74,78,
%T A144043 82,84,86,90,94,100,106,112,118,120,122,128,134,138,142,144,146,152,
%U A144043 158,162,166,172,178,186,194,198,202,204
%N A144043 a(2n-1) = 2*prime(n), a(2n) = prime(n) + prime(n+1).
%C A144043 Previous name was "Sum of the middle pair in the n-term sequence 2, 3, 5, ..., prime(n)." - _Jon E. Schoenfield_, Oct 12 2015
%C A144043 The bisections are the doubled primes (A100484) and the sums of adjacent primes (A001043). - _R. J. Mathar_, Sep 11 2011
%H A144043 Paolo Xausa, <a href="/A144043/b144043.txt">Table of n, a(n) for n = 1..10000</a>
%F A144043 a(2n-1) = 2 prime(n), a(2n) = prime(n) + prime(n+1), n = 1,2,... - _Zak Seidov_, Jan 15 2014
%F A144043 a(n) = 2*A063934(n-1) for n>2. - _Michel Marcus_, Oct 13 2015
%e A144043 4 = sumtwice(2); 5 = sum(2,3); 6 = 2, sumtwice(3), 5, 7; 8 = 2, sum(3,5), 7, 11;
%p A144043 A144043 := proc(n) ithprime(ceil((n+1)/2))+ithprime(ceil(n/2)) ; end proc: # _R. J. Mathar_, Sep 11 2011
%t A144043 With[{p=Prime[Range[50]]},Riffle[2p,ListConvolve[{1,1},p]]] (* _Paolo Xausa_, Nov 02 2023 *)
%o A144043 (MATLAB) clc clear all aP= [primes(1000)]; qN= numel(aP); kL=[]; %init empty result for nn= 1:qN %Loop to sum the central pairs auxT= ceil((nn+1)/2); auxL= ceil(nn/2); kL= [kL; aP(auxL)+aP(auxT)]; end kL %kL is the result
%K A144043 easy,nonn
%O A144043 1,1
%A A144043 Raul Rato (rtrato(AT)yahoo.com), Sep 08 2008
%E A144043 Removed initial terms that regarded 1 as a prime. - _R. J. Mathar_, Sep 11 2011
%E A144043 Comments edited by _Zak Seidov_, Jan 15 2014
%E A144043 Name changed (based on formula from _Zak Seidov_) by _Jon E. Schoenfield_, Oct 12 2015