A123078 Integers that are the arithmetic mean of 1000 consecutive primes.

10820, 15682, 19672, 23340, 25067, 33873, 37387, 39377, 47782, 59635, 75249, 82619, 86378, 87303, 89198, 92217, 97495, 111989, 131987, 133441, 162286, 164644, 178666, 181532, 182196, 200088, 203450, 215280, 215612, 218527, 221526, 229733

Offset

1,1

Comments

Corresponding indices of the first primes are: 812, 1323, 1731, 2097, 2268, 3121, 3456, 3645, 4428, 5518, 6914, 7569, 7899, 7980, 8146, 8412, 8875, ... .

Links

Zak Seidov, Table of n, a(n) for n = 1..1000

Formula

Conjecture: a(n) ~ 1000 n log n. - Charles R Greathouse IV, Oct 23 2012

Example

(p(812)+p(813)+...+p(812+998)+p(812+999))/1000=10820, p(n)=n-th prime.

Mathematica

Select[Table[Sum[Prime[k], {k, n, n + 999}]/1000, {n, 50000}], IntegerQ] (* Elizabeth A. Blickley (Elizabeth.Blickley(AT)gmail.com), Oct 10 2006 *)
Select[Mean/@Partition[Prime[Range[25000]], 1000, 1], IntegerQ] (* Harvey P. Dale, Jul 27 2022 *)

Crossrefs

Cf. A102655, A122040, A122480, A122808.

Sequence in context: A190115 A203394 A144716 * A235254 A237190 A065321

Adjacent sequences: A123075 A123076 A123077 * A123079 A123080 A123081

Keyword

nonn

Author

Zak Seidov, Sep 27 2006

Extensions

More terms from Elizabeth A. Blickley (Elizabeth.Blickley(AT)gmail.com), Oct 10 2006

Status

approved