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

4, 5, 6, 8, 10, 12, 14, 18, 22, 24, 26, 30, 34, 36, 38, 42, 46, 52, 58, 60, 62, 68, 74, 78, 82, 84, 86, 90, 94, 100, 106, 112, 118, 120, 122, 128, 134, 138, 142, 144, 146, 152, 158, 162, 166, 172, 178, 186, 194, 198, 202, 204

Offset

1,1

Comments

Previous name was "Sum of the middle pair in the n-term sequence 2, 3, 5, ..., prime(n)." - Jon E. Schoenfield, Oct 12 2015

The bisections are the doubled primes (A100484) and the sums of adjacent primes (A001043). - R. J. Mathar, Sep 11 2011

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Formula

a(2n-1) = 2 prime(n), a(2n) = prime(n) + prime(n+1), n = 1,2,... - Zak Seidov, Jan 15 2014

a(n) = 2*A063934(n-1) for n>2. - Michel Marcus, Oct 13 2015

Example

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

Maple

A144043 := proc(n) ithprime(ceil((n+1)/2))+ithprime(ceil(n/2)) ; end proc: # R. J. Mathar, Sep 11 2011

Mathematica

With[{p=Prime[Range[50]]}, Riffle[2p, ListConvolve[{1, 1}, p]]] (* Paolo Xausa, Nov 02 2023 *)

Prog

(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

Crossrefs

Sequence in context: A295485 A226746 A206416 * A139446 A274918 A277736

Adjacent sequences: A144040 A144041 A144042 * A144044 A144045 A144046

Keyword

easy,nonn

Author

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

Extensions

Removed initial terms that regarded 1 as a prime. - R. J. Mathar, Sep 11 2011

Comments edited by Zak Seidov, Jan 15 2014

Name changed (based on formula from Zak Seidov) by Jon E. Schoenfield, Oct 12 2015

Status

approved