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A021093
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Decimal expansion of 1/89.
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7
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0, 1, 1, 2, 3, 5, 9, 5, 5, 0, 5, 6, 1, 7, 9, 7, 7, 5, 2, 8, 0, 8, 9, 8, 8, 7, 6, 4, 0, 4, 4, 9, 4, 3, 8, 2, 0, 2, 2, 4, 7, 1, 9, 1, 0, 1, 1, 2, 3, 5, 9, 5, 5, 0, 5, 6, 1, 7, 9, 7, 7, 5, 2, 8, 0, 8, 9, 8, 8, 7, 6, 4, 0, 4, 4, 9, 4, 3, 8, 2, 0, 2, 2, 4, 7, 1, 9, 1, 0, 1, 1, 2, 3, 5, 9, 5, 5, 0, 5
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Note the strange resemblance to the Fibonacci numbers (A000045). In fact 1/89 = sum (Fibonacci(i)/10^(i+1)). (In the same way, the Lucas numbers sum up to 120/89) - Johan Claes (Johan.Claes(AT)luc.ac.be), Jun 11 2004
In the Red Zen reference, the decimal expansion of 1/89 and its relation to the Fibonacci sequence is discussed; also primes of the form Floor(1/89 * 10^n) are given for n = 3, 5 and 631. - Jason Earls (zevi_35711(AT)yahoo.com), May 28 2007
The 44-digit cycle 1,0,1,1,2,3,5,9,5,5,0,5,6,1,7,9,7,7,5,2,8,0,8,9,8,8,7,6,4, 0,4,4,9,4,3,8,2,0,2,4,4,7,1,9 in this sequence and the others based on eighty-ninths, gives the successive digits of the smallest integer which is multiplied by nine when the final digit is moved from the right hand end to the left hand end. - Ian Duff (ianfduff(AT)yahoo.co.uk), Jan 09 2009
Generalization:
1/89 = sum (Fibonacci(i)/10^(i+1)), (this sequence)
1/9899 = sum (Fibonacci(i)/100^(i+1)),
1/998999 = sum (Fibonacci(i)/1000^(i+1)),
1/99989999 = sum (Fibonacci(i)/10000^(i+1)), ... - Daniel Forgues, Oct 28, 2011
Generalization:
1/89 = sum (11^i/100^(i+1)), i >= 0, (this sequence)
1/989 = sum (11^i/1000^(i+1)), i >= 0,
1/9989 = sum (11^i/10000^(i+1)), i >= 0, ... - Daniel Forgues, Oct 28, 2011
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REFERENCES
| J. Earls, Red Zen, Lulu Press, NY, 2007, pp. 47-48. ISBN: 978-1-4303-2017-3.
Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 66.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1).
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PROG
| (PARI) 1/89. \\ Charles R Greathouse IV, Dec 05 2011
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CROSSREFS
| Cf. A000045.
Sequence in context: A064358 A109736 A119628 * A011026 A069805 A123923
Adjacent sequences: A021090 A021091 A021092 * A021094 A021095 A021096
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KEYWORD
| nonn,cons,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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