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

Author

Zak Seidov, Sep 27 2006

Keywords

• nonn

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, ... .

Examples

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

Links

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

Crossrefs

Cf. A102655, A122040, A122480, A122808.

Programs

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 *)

Formula

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

Extensions

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