A229470 - OEIS

%I #21 Oct 09 2013 04:58:41

%S 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 94,99,105,112,121,123,126,130,135,141,148,156,166,168,171,175,180,

%U 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 Positions of 2 in decimal expansion of 0.1231232331232332333..., whose definition is given below.

%C 0.1231232331232332333... = sum_{k=0..infinity, 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 a((n^2+n+2m-2)/2) = (n^3+6n^2+3m^2+11n-3m+6)/6; n+2>=m>=2.

%F a(n) = sum_(k=0..n-1, 1 + A002262(k) + A010054(k)*(sqrt(1+8k)+1)/2 ).

%o (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 easy,nonn,base

%O 1,1

%A _Jiri Klepl_, Sep 24 2013

%E Formula corrected by _Ralf Stephan_, Oct 09 2013