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, 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

1,3

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.

Links

Table of n, a(n) for n=1..87.

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);

Crossrefs

Sequence in context: A364502 A141749 A117017 * A058969 A021113 A019948

Adjacent sequences: A244858 A244859 A244860 * A244862 A244863 A244864

Keyword

nonn,easy,cons,base

Author

Paolo P. Lava, Nov 12 2014

Status

approved