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A035026
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Number of times that i and 2n-i are both prime, for i=1,...2n-1.
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11
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0, 1, 1, 2, 3, 2, 3, 4, 4, 4, 5, 6, 5, 4, 6, 4, 7, 8, 3, 6, 8, 6, 7, 10, 8, 6, 10, 6, 7, 12, 5, 10, 12, 4, 10, 12, 9, 10, 14, 8, 9, 16, 9, 8, 18, 8, 9, 14, 6, 12, 16, 10, 11, 16, 12, 14, 20, 12, 11, 24, 7, 10, 20, 6, 14, 18, 11, 10, 16, 14, 15, 22, 11, 10, 24, 8, 16, 22, 9, 16, 20, 10
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| a(n) is the convolution of terms 1 to 2n of the characteristic function of the primes, A010051, with itself. Related to Goldbach's conjecture that every even number can be expressed as the sum of two primes. - T. D. Noe (noe(AT)sspectra.com), Aug 01 2002
The following sequences all appear to have the same parity (with an extra zero term at the start of A010051): A010051, A061007, A035026, A069754, A071574. - Jeremy Gardiner (jeremy.gardiner(AT)btinternet.com), Aug 09, 2002
Total number of printer jobs in all possible schedules for n time slots in the first-come-first-served (FCFS) policy.
a(n) = sum (A010051(2*n - p): p prime < 2*n). [Reinhard Zumkeller, Oct 19 2011]
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for sequences related to Goldbach conjecture
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FORMULA
| For n > 1, a(n) = 2*A045917(n) - A010051(n).
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MATHEMATICA
| For[lst={}; n=1, n<=100, n++, For[cnt=0; i=1, i<=2n-1, i++ If[PrimeQ[i]&&PrimeQ[2n-i], cnt++ ]]; AppendTo[lst, cnt]]; lst
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PROG
| (Haskell)
a035026 n = sum $ map (a010051 . (2*n -)) $ takeWhile (< 2*n) a000040_list
-- Reinhard Zumkeller, Oct 19 2011
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CROSSREFS
| Cf. A010051. Essentially the same as A002372.
Sequence in context: A129600 A081388 A002372 * A173540 A070770 A071487
Adjacent sequences: A035023 A035024 A035025 * A035027 A035028 A035029
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KEYWORD
| easy,nonn
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AUTHOR
| Gordon R. Bower (siegmund(AT)mosquitonet.com)
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EXTENSIONS
| Corrected by T. D. Noe (noe(AT)sspectra.com), May 05 2002
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