A213174 a(n) is the smallest number that is the sum of both 2n-1 and 2n+1 consecutive primes.

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

Offset: 1

Author

Zak Seidov, Mar 07 2013

Keywords

• nonn

Examples

			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.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 2449 terms from Robert G. Wilson v)

Programs

Mathematica

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 *)