A222592 Smallest integer that is a sum of 2*k consecutive primes for each k = 1..n.

5, 36, 8412, 227304, 39851304, 1622295444, 55789710106764

Offset: 1

Author

Zak Seidov, Feb 26 2013

Keywords

• nonn
• more

Examples

			a(1) = 5 = 2+3;
a(2) = 36 = 17+19 = 5+7+11+13;
a(3) = 8412 = 4201 + 4211 =
  2089 + 2099 + 2111 + 2113 =
  1373 + 1381 + 1399 + 1409 + 1423 + 1427;
a(4) = 227304 = 113647 + 113657 =
  56813 +  56821 + 56827 + 56843 =
  37861 + 37871 + 37879 + 37889 + 37897 + 37907 =
  28387 + 28393 + 28403 + 28409 +
  28411 + 28429 + 28433 + 28439;
a(5) = 39851304 = 19925627 + 19925677 =
  9962809 + 9962819 + 9962837 + 9962839 =
  6641839 + 6641851 + 6641867 + 6641891 + 6641903 + 6641953 =
  4981367 + 4981373 + 4981387 + 4981393 +
  4981423 + 4981441 + 4981451 + 4981469 =
  3985063 + 3985067 + 3985073 + 3985087 + 3985099 +
  3985103 + 3985181 + 3985207 + 3985211 + 3985213.
The initial primes of the 6 tuples corresponding to a(6) are 811147721, 405573827, 270382529, 202786813, 162229471, and 135191207. - _Giovanni Resta_, Feb 26 2013
		

Crossrefs

Cf. A222564, A288340.

Programs

Mathematica

a[n_] := Block[{t, w}, t = Table[{Total@(w = Prime@Range@(2*i)), w}, {i, n}]; While[Length@Union[First /@ t] > 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 26 2013 *)

Extensions

a(6) from Giovanni Resta, Feb 26 2013

a(7) from Max Alekseyev, Feb 12 2023