A022002 -id:A022002 - cp's OEIS frontend

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

Jean-François Alcover, Jan 31 2014

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.

			0.0001000200040008001600320064012802560512102420484096819363872774554910982...

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

Cf. A021102, A022002.

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

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

A021102 Decimal expansion of 1/98.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane

Generalization:
  1/8 = sum (2^i/10^(i+1)), i >= 0,
  1/98 = sum (2^i/100^(i+1)), i >= 0, (this sequence)
  1/998 = sum (2^i/1000^(i+1)), i >= 0,
  1/9998 = sum (2^i/10000^(i+1)), i >= 0, ... - Daniel Forgues, Oct 28 2011

Mario Raso, Integer Sequences in Cryptography: A New Generalized Family and its Application, Ph. D. Thesis, Sapienza University of Rome (Italy 2025). See p. 9.
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1).

Cf. A020821 (1/8), A022002 (1/998), A236799 (1/9998).

Join[{0},RealDigits[1/98,10,120][[1]]] (* Harvey P. Dale, May 29 2013 *)

cp's OEIS Frontend

A236799 Decimal expansion of 1/9998.

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