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A244861 Consider the concatenation in ascending order of the first x natural numbers and then concatenate its reverse. Sequence gives the decimal expansion of the sum of the reciprocals of such numbers.

%I A244861 #20 Jul 28 2025 16:11:10
%S A244861 0,9,1,7,3,6,2,8,2,4,7,4,1,9,3,3,7,2,5,0,0,2,9,5,9,8,4,2,9,8,2,9,3,9,
%T A244861 5,0,9,3,2,0,7,5,2,7,3,0,0,9,2,8,1,4,2,5,7,2,9,3,5,1,1,3,6,0,3,2,9,5,
%U A244861 6,0,8,7,6,6,6,9,6,7,8,2,7,0,7,6,2,4
%N A244861 Consider the concatenation in ascending order of the first x natural numbers and then concatenate its reverse. Sequence gives the decimal expansion of the sum of the reciprocals of such numbers.
%C A244861 Decimal expansion of 1/11 + 1/1221 + 1/123321 + ... + 1/123456789987654321 + 1/1234567891001987654321 + 1/12345678910111101987654321 + 1/123456789101112211101987654321 + ...
%C A244861 0.0917362824741933725002959842982939... = [0, 10, 1, 9, 12, 4, 1, 3, 6].
%C A244861 Rational approximation up to the 11th decimal digit: 14649/159686.
%e A244861 0.091736282474193372500295984298293950932...
%p A244861 with(numtheory): T:=proc(w) local x,y,z; x:=w; y:=0;
%p A244861 for z from 1 to ilog10(x)+1 do y:=y*10+(x mod 10); x:=trunc(x/10); od; y: end:
%p A244861 P:=proc(q) local a,b,n; a:=0; b:=0; for n from 1 to q do
%p A244861 a:=trunc(a/10^((ilog10(a)+1)/2))*10^(ilog10(n)+1)+n; a:=a*10^(ilog10(a)+1)+T(a);
%p A244861 b:=b+1/a; od; evalf(b,500); end: P(300);
%Y A244861 Cf. A259937.
%K A244861 nonn,easy,cons,base
%O A244861 0,2
%A A244861 _Paolo P. Lava_, Nov 12 2014