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A213174
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a(n) is the smallest number that is the sum of both 2n-1 and 2n+1 consecutive primes.
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3
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23, 83, 119, 401, 1025, 3321, 863, 5683, 1523, 3397, 3979, 8983, 7901, 21775, 11131, 9073, 14699, 16277, 30895, 9167, 15947, 40091, 105131, 54923, 14413, 15605, 122135, 29775, 173649, 80841, 99149, 56495, 189807, 46421, 290203, 158741, 56099, 276535, 189869
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OFFSET
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1,1
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LINKS
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EXAMPLE
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23 = 5 + 7 + 11, 83 = 23 + 29 + 31 = 11 + 13 + 17 + 19 + 23,
119 = 17 + 19 + 23 + 29 + 31 = 7 + 11 + 13 + 17 + 19 + 23 + 29.
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MATHEMATICA
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pr = Prime[Range[1, 100]]; Table[{n, Intersection[(Plus @@@ Partition[pr, 2 n - 1, 1]), Plus @@@ Partition[pr, 2 n + 1, 1]][[1]]}, {n, 40}] (* or *)
S = Accumulate@ Prime@ Range@ 64000; Table[A = <||>; v = 0; Do[ A[S[[k + 2 n + 1]] - S[[k]]] = 0; t = S[[k + 2 n - 1]] - S[[k]]; If[KeyExistsQ[A, t], v = t; Break[]], {k, 64000 -2*n-1}]; If[v == 0, Break[], v], {n, 1000}] (* Giovanni Resta, Jun 08 2017 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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