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A144043
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Sum of the middle pair in the partial sequence 2, 3, 5, .. ,prime(n).
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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| An exotic sequence with a tantalizing non-regularity. It is strictly nondecreasing (very easy to show). The first order differences (1, 1, 1, 1, 2, 2, 2, 2, 4, 4, 2, 2, 4, 4, 2, 2, 4, 4, ...) are also very erratic.
The bisections are the doubled primes (A100484) and the sums of neighboring primes (A001043). - R. J. Mathar, Sep 11 2011
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EXAMPLE
| 4= sumtwice(2); 5= sum(2,3); 6= 2, sumtwice(3), 5, 7; 8= 2, sum(3,5), 7, 11;
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MAPLE
| A144043 := proc(n) ithprime(ceil((n+1)/2))+ithprime(ceil(n/2)) ; end proc: - R. J. Mathar, Sep 11 2011
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PROG
| (Other) %Matlab source code 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
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CROSSREFS
| Sequence in context: A053427 A037354 A206416 * A035065 A035067 A027698
Adjacent sequences: A144040 A144041 A144042 * A144044 A144045 A144046
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KEYWORD
| easy,nonn
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AUTHOR
| Raul Rato (rtrato(AT)yahoo.com), Sep 08 2008
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EXTENSIONS
| Removed initial terms that regarded 1 as a prime. - R. J. Mathar, Sep 11 2011
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