A222564 Least integer that is a sum of 2*k - 1 consecutive primes for k = 1..n.

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

Links

Table of n, a(n) for n=1..7.

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

Adjacent sequences: A222561 A222562 A222563 * A222565 A222566 A222567

Keyword

nonn,more

Author

Zak Seidov, Feb 27 2013

Extensions

a(6)-a(7) from Giovanni Resta, Feb 27 2013

Status

approved