A144043 - OEIS

%I #31 Nov 02 2023 23:41:46

%S 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 82,84,86,90,94,100,106,112,118,120,122,128,134,138,142,144,146,152,

%U 158,162,166,172,178,186,194,198,202,204

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

%C 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 The bisections are the doubled primes (A100484) and the sums of adjacent primes (A001043). - _R. J. Mathar_, Sep 11 2011

%H Paolo Xausa, <a href="/A144043/b144043.txt">Table of n, a(n) for n = 1..10000</a>

%F a(2n-1) = 2 prime(n), a(2n) = prime(n) + prime(n+1), n = 1,2,... - _Zak Seidov_, Jan 15 2014

%F a(n) = 2*A063934(n-1) for n>2. - _Michel Marcus_, Oct 13 2015

%e 4 = sumtwice(2); 5 = sum(2,3); 6 = 2, sumtwice(3), 5, 7; 8 = 2, sum(3,5), 7, 11;

%p A144043 := proc(n) ithprime(ceil((n+1)/2))+ithprime(ceil(n/2)) ; end proc: # _R. J. Mathar_, Sep 11 2011

%t With[{p=Prime[Range[50]]},Riffle[2p,ListConvolve[{1,1},p]]] (* _Paolo Xausa_, Nov 02 2023 *)

%o (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 easy,nonn

%O 1,1

%A Raul Rato (rtrato(AT)yahoo.com), Sep 08 2008

%E Removed initial terms that regarded 1 as a prime. - _R. J. Mathar_, Sep 11 2011

%E Comments edited by _Zak Seidov_, Jan 15 2014

%E Name changed (based on formula from _Zak Seidov_) by _Jon E. Schoenfield_, Oct 12 2015