This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A123078 #22 Jan 06 2025 06:17:13
%S A123078 10820,15682,19672,23340,25067,33873,37387,39377,47782,59635,75249,
%T A123078 82619,86378,87303,89198,92217,97495,111989,131987,133441,162286,
%U A123078 164644,178666,181532,182196,200088,203450,215280,215612,218527,221526,229733
%N A123078 Integers that are the arithmetic mean of 1000 consecutive primes.
%C A123078 Corresponding indices of the first primes are: 812, 1323, 1731, 2097, 2268, 3121, 3456, 3645, 4428, 5518, 6914, 7569, 7899, 7980, 8146, 8412, 8875, ... .
%H A123078 Zak Seidov, <a href="/A123078/b123078.txt">Table of n, a(n) for n = 1..1000</a>
%F A123078 Conjecture: a(n) ~ 1000 n log n. - _Charles R Greathouse IV_, Oct 23 2012
%e A123078 (p(812)+p(813)+...+p(812+998)+p(812+999))/1000=10820, p(n)=n-th prime.
%t A123078 Select[Table[Sum[Prime[k], {k, n, n + 999}]/1000, {n, 50000}], IntegerQ] (* Elizabeth A. Blickley (Elizabeth.Blickley(AT)gmail.com), Oct 10 2006 *)
%t A123078 Select[Mean/@Partition[Prime[Range[25000]],1000,1],IntegerQ] (* _Harvey P. Dale_, Jul 27 2022 *)
%Y A123078 Cf. A102655, A122040, A122480, A122808.
%K A123078 nonn
%O A123078 1,1
%A A123078 _Zak Seidov_, Sep 27 2006
%E A123078 More terms from Elizabeth A. Blickley (Elizabeth.Blickley(AT)gmail.com), Oct 10 2006