A236799 Decimal expansion of 1/9998.

0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 8, 0, 0, 1, 6, 0, 0, 3, 2, 0, 0, 6, 4, 0, 1, 2, 8, 0, 2, 5, 6, 0, 5, 1, 2, 1, 0, 2, 4, 2, 0, 4, 8, 4, 0, 9, 6, 8, 1, 9, 3, 6, 3, 8, 7, 2, 7, 7, 4, 5, 5, 4, 9, 1, 0, 9, 8, 2, 1, 9, 6, 4, 3, 9, 2, 8, 7, 8, 5, 7, 5, 7, 1, 5, 1, 4, 3, 0, 2, 8, 6, 0, 5, 7, 2, 1, 1, 4, 4, 2

Offset

0,8

Comments

Generalization

1/8 = Sum_{i >= 0} 2^i/10^(i+1),

1/98 = Sum_{i >= 0} 2^i/100^(i+1), (A021102),

1/998 = Sum_{i >= 0} 2^i/1000^(i+1), (A022002),

1/9998 = Sum_{i >= 0} 2^i/10000^(i+1), (this sequence).

A "curiosity": the first 13 groups of digits in groups of 4 give the successive powers of 2:

0, 0, 0, 1,

0, 0, 0, 2,

0, 0, 0, 4,

0, 0, 0, 8,

0, 0, 1, 6,

0, 0, 3, 2,

0, 0, 6, 4,

0, 1, 2, 8,

0, 2, 5, 6,

0, 5, 1, 2,

1, 0, 2, 4,

2, 0, 4, 8,

4, 0, 9, 6, <-- the last explicit power of 2

8, 1, 9, 3,

6, 3, 8, 7,

etc.

Links

Jean-François Alcover, Table of n, a(n) for n = 0..359

Example

0.0001000200040008001600320064012802560512102420484096819363872774554910982...

Mathematica

Join[{0, 0, 0}, RealDigits[1/9998, 10, 102] // First]

Prog

(PARI) 1/9998. \\ Charles R Greathouse IV, Feb 26 2014

Crossrefs

Cf. A021102, A022002.

Sequence in context: A134309 A051516 A386279 * A208274 A208604 A127391

Adjacent sequences: A236796 A236797 A236798 * A236800 A236801 A236802

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jan 31 2014

Status

approved