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 A229470 #25 Feb 24 2025 06:26:23
%S A229470 2,5,7,11,13,16,21,23,26,30,36,38,41,45,50,57,59,62,66,71,77,85,87,90,
%T A229470 94,99,105,112,121,123,126,130,135,141,148,156,166,168,171,175,180,
%U A229470 186,193,201,210,221,223,226,230,235,241,248,256,265,275,287,289,292,296,301,307,314,322,331,341,352,365,367,370,374,379,385
%N A229470 Positions of 2 in decimal expansion of 0.1231232331232332333..., whose definition is given below.
%C A229470 0.1231232331232332333... = Sum_{k>=0} 10^(-(k + 3)! / (3! * k!)) * (1 + 10 * Sum_{l=2..k+2} 10^(-(l^2 + l) / 2) * ((10^l - 1) / 3 - 10^(l - 1))).
%F A229470 a((n^2+n+2m-2)/2) = (n^3+6n^2+3m^2+11n-3m+6)/6; n+2>=m>=2.
%F A229470 a(n) = Sum_{k=0..n-1} ( 1 + A002262(k) + A010054(k)*(sqrt(1+8*k)+1)/2 ).
%o A229470 (PARI) a(n)=sum(k=0,n-1,1+k-binomial(round(sqrt(2+2*k)),2)+issquare(8*k+1)*(sqrtint(1+8*k)+1)/2) /* _Ralf Stephan_, Oct 09 2013 */
%K A229470 easy,nonn,base
%O A229470 1,1
%A A229470 _Jiri Klepl_, Sep 24 2013
%E A229470 Formula corrected by _Ralf Stephan_, Oct 09 2013