A228669 Numbers k for which sum{prime(2*k) - prime(2*k-1)} is prime.

2, 3, 4, 5, 6, 9, 14, 16, 19, 21, 23, 25, 26, 27, 32, 34, 35, 36, 37, 38, 43, 44, 49, 50, 55, 63, 64, 65, 70, 73, 76, 81, 96, 101, 107, 113, 121, 126, 129, 132, 135, 145, 147, 152, 154, 157, 158, 160, 161, 166, 171, 174, 176, 179, 180, 183, 187, 196, 197

Offset: 1

Author

Clark Kimberling, Oct 01 2013

Keywords

• nonn

Examples

			a(6) = 9 because 3-2 + 7-5 + 13-11 + 19-17 + 29-23 + 37-31 = 19 =
A077133(6) is a prime.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A077133.

Programs

Mathematica

z = 300; f[n_] := Sum[Prime[2 k] - Prime[2 k - 1], {k, 1, n}]
Table[f[n], {n, 1, z}]  (* A077133 *)
g[n_] := If[PrimeQ[f[n]], 1, 0]; t = Table[g[n], {n, 1, z}]; Flatten[Position[t, 1]]
Position[Accumulate[#[[2]]-#[[1]]&/@Partition[Prime[Range[400]],2]], ?PrimeQ]//Flatten (* _Harvey P. Dale, Jul 26 2018 *)