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%I #34 Feb 28 2013 21:36:35
%S 2,23,83,311,28382041,1128722657,460787266801
%N Least integer that is a sum of 2*k - 1 consecutive primes for k = 1..n.
%C For a(5) = 28382041, the first members of the sets are 9460669, 5676371, 4054499, and 3153499.
%C For a(6) the first members of the sets are 376240871, 225744509, 161246051, 125413559 and 102611081. For a(7) they are 153595755589, 92157453257, 65826752333, 51198585101, 41889751411 and 35445174181 - _Giovanni Resta_, Feb 27 2013
%e a(1) = 2;
%e a(2) = 23 = 5 + 7 + 11;
%e a(3) = 83 = 23 + 29 + 31 = 11 + 13 + 17 + 19 + 23;
%e a(4) = 311 = 101 + 103 + 107 = 53 + 59 + 61 + 67 + 71 = 31 + 37 + 41 + 43 + 47 + 53 + 59.
%t pr = Prime[Range[1000]]; tu[n_]:=(Total /@ Partition[pr, n, 1])
%t Intersection[tu[3],tu[5],tu[7]][[1]] (* gives a(3) = 311 - _Zak Seidov_, Feb 27 2013*)
%t a[n_] := If[n == 1, 2, Block[{t, w}, t = Table[{Total@(w = Prime@ Range@(2*i + 1)), w}, {i, n - 1}]; While[Length@Union[First /@ t] > 1 || ! PrimeQ@t[[1, 1]], t = Sort@t; w = NextPrime@t[[1, 2, -1]]; t[[1, 1]] += w - t[[1, 2, 1]]; t[[1, 2]] = Append[Rest@t[[1, 2]], w]]; t[[1, 1]]]]; Array[a, 4] (* _Giovanni Resta_, Feb 27 2013 *)
%Y Cf. A222592.
%K nonn,more
%O 1,1
%A _Zak Seidov_, Feb 27 2013
%E a(6)-a(7) from _Giovanni Resta_, Feb 27 2013
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