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A222564
Least integer that is a sum of 2*k - 1 consecutive primes for k = 1..n.
3
2, 23, 83, 311, 28382041, 1128722657, 460787266801
OFFSET
1,1
COMMENTS
For a(5) = 28382041, the first members of the sets are 9460669, 5676371, 4054499, and 3153499.
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
EXAMPLE
a(1) = 2;
a(2) = 23 = 5 + 7 + 11;
a(3) = 83 = 23 + 29 + 31 = 11 + 13 + 17 + 19 + 23;
a(4) = 311 = 101 + 103 + 107 = 53 + 59 + 61 + 67 + 71 = 31 + 37 + 41 + 43 + 47 + 53 + 59.
MATHEMATICA
pr = Prime[Range[1000]]; tu[n_]:=(Total /@ Partition[pr, n, 1])
Intersection[tu[3], tu[5], tu[7]][[1]] (* gives a(3) = 311 - Zak Seidov, Feb 27 2013*)
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 *)
CROSSREFS
Cf. A222592.
Sequence in context: A209194 A097232 A339474 * A099134 A069152 A131464
KEYWORD
nonn,more
AUTHOR
Zak Seidov, Feb 27 2013
EXTENSIONS
a(6)-a(7) from Giovanni Resta, Feb 27 2013
STATUS
approved