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 A385994 #36 Aug 04 2025 01:05:29
%S A385994 2,10,12,19,23,26,29,32,40,48,50,53,53,61,62,65,74,75,79,85,86,92,95,
%T A385994 102,111,111,115,119,128,133,134,139,144,146,151,160,165,172,179,186,
%U A385994 190,195,197,201,206,215,219,222,229,234,243,248,250,253,261,269,276,283,287
%N A385994 Lexicographically greatest increasing expansion Pi = Sum_{n>=0} a(n)/10^n, where a(n+1) >= a(n).
%C A385994 Each successive term is maximal consistent with the sum approaching Pi from below.
%C A385994 Each difference d = a(n) - a(n-1) (and reckoning an a(-1)=0) effectively repeats in all subsequent terms and so contributes (10/9)*d/10^n into the sum, and for that reason those differences are the decimal digits of (9/10)*Pi and the terms are partial sums of those digits.
%H A385994 Pierre-Alain Sallard, <a href="/A385994/a385994.pdf">Proof</a>
%F A385994 a(n) = Sum_{i=0..n} A229939(i+1).
%t A385994 a[n_]:=Sum[Part[RealDigits[9*Pi, n+1][[1]],i],{i,1,n+1}]; Array[a,59,0] (* _Stefano Spezia_, Jul 14 2025 *)
%Y A385994 Cf. A000796.
%Y A385994 Partial sums of A229939.
%K A385994 nonn,base,easy
%O A385994 0,1
%A A385994 _Pierre-Alain Sallard_, Jul 14 2025