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A228669 Numbers k for which sum{prime(2*k) - prime(2*k-1)} is prime. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

EXAMPLE

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

A077133(6) is a prime.

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 *)

CROSSREFS

Cf. A077133.

Sequence in context: A017833 A114044 A113444 * A308020 A200444 A307972

Adjacent sequences:  A228666 A228667 A228668 * A228670 A228671 A228672

KEYWORD

nonn

AUTHOR

Clark Kimberling, Oct 01 2013

STATUS

approved

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Last modified July 24 05:23 EDT 2021. Contains 346273 sequences. (Running on oeis4.)