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Search: id:A163059
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| A163059 |
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An alternating sum from 4*n-3 up to the smaller of the n-th twin primes. |
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+0
1
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| 2, 5, 10, 15, 23, 31, 42, 50, 67, 72, 89, 97, 114, 122, 127, 144, 152, 169, 177, 194, 214, 252, 260, 277, 309, 335, 352, 363, 377, 388, 465, 473, 478, 495, 509, 580, 588, 599, 607, 624, 656, 697, 723, 731, 739, 750, 806, 820, 837, 842, 904, 912, 938, 955, 969, 1004
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Consider the alternating sums S(l,h) = -sum_{j=l..u} j*(-1)^j = A001057(u)-A001057(l-1).
a(n) is this sum for a lower limit of 4n-3 = A016813(n-1) and an upper limit of A001359(n).
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FORMULA
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a(n) = A001057(A001359(n))-A001057(4*n-4).
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EXAMPLE
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a(1)=1-2+3=2. a(2)=5. a(3)=9-10+11. a(4)=13-14+15-16+17=15. a(5)=17-18+19-20+21-22+23-24+25-26+27-28+29=20.
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MAPLE
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A001057 := proc(n) (-1)^(n+1)*floor((n+1)/2) ; end:
A001359 := proc(n) local a; option remember ; if n = 1 then 3; else for a from procname(n-1)+1 do if isprime(a) and isprime(a+2) then RETURN(a) ; fi; od: fi; end:
A163059 := proc(n) A001057(A001359(n))-A001057(4*n-4) ; end: seq(A163059(n), n=1..80) ; # R. J. Mathar, Aug 02 2009
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CROSSREFS
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Cf. A001359, A016813.
Sequence in context: A080551 A008822 A013927 this_sequence A099738 A117582 A002134
Adjacent sequences: A163056 A163057 A163058 this_sequence A163060 A163061 A163062
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KEYWORD
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nonn
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AUTHOR
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Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jul 20 2009
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EXTENSIONS
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a(5) and a(23)-a(25) corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 02 2009
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