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.

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, 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, 6, 0, 8, 7, 6, 6, 6, 9, 6, 7, 8, 2, 7, 0, 7, 6, 2, 4

Offset: 0

Author

Paolo P. Lava, Nov 12 2014

Keywords

• nonn
• easy
• cons
• base

Comments

Decimal expansion of 1/11 + 1/1221 + 1/123321 + ... + 1/123456789987654321 + 1/1234567891001987654321 + 1/12345678910111101987654321 + 1/123456789101112211101987654321 + ...

0.0917362824741933725002959842982939... = [0, 10, 1, 9, 12, 4, 1, 3, 6].

Rational approximation up to the 11th decimal digit: 14649/159686.

Examples

			0.091736282474193372500295984298293950932...
		

Crossrefs

Cf. A259937.

Programs

Maple

with(numtheory): T:=proc(w) local x,y,z; x:=w; y:=0;
for z from 1 to ilog10(x)+1 do y:=y*10+(x mod 10); x:=trunc(x/10); od; y: end:
P:=proc(q) local a,b,n; a:=0; b:=0; for n from 1 to q do
a:=trunc(a/10^((ilog10(a)+1)/2))*10^(ilog10(n)+1)+n; a:=a*10^(ilog10(a)+1)+T(a);
b:=b+1/a; od; evalf(b,500); end: P(300);