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Search: id:A101641
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| A101641 |
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Positive integers n for which n = f(n), where f(n) is the total number of 4's required when writing out all numbers between 0 and n. |
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11
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| 499999984, 499999985, 499999986, 499999987, 499999988, 499999989, 499999990, 499999991, 499999992, 499999993, 500000000, 10000000000, 10499999984, 10499999985, 10499999986, 10499999987, 10499999988, 10499999989
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Related to a problem posed by Google and discussed on the MathWorld link.
Together with the b-file, this gives the complete list of all 47 positive numbers n such that n is equal to the number of 4's in the decimal digits of all numbers <= n. - Daniel Hirschberg (dan(AT)ics.uci.edu), May 05 2007
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LINKS
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Daniel Hirschberg (dan(AT)ics.uci.edu), May 05 2007, Table of n, a(n) for n = 1..47
Mathworld, A problem posed by Google
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FORMULA
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a(n) = 499999983 + n, n <= 10; a(n) = 500000000, n = 11
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EXAMPLE
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a(1) = 499999984, since writing out all numbers from 0 to 499999984 requires that 499999984 4's be used and since 499999984 is the first such positive integer.
a(4)=499999987 because the number of 4's in the decimal digits of the numbers from 1 to 499999987 is 499999987 and this is the 4th such number.
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CROSSREFS
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Cf. A014778 for proof these sequences are finite; Also A101639, A101640, A130427, A130428, A130429, A130430, A130431; cf. A130432 for the number of numbers in these sequences.
Sequence in context: A127888 A072232 A011523 this_sequence A034617 A135977 A011579
Adjacent sequences: A101638 A101639 A101640 this_sequence A101642 A101643 A101644
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KEYWORD
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fini,nonn
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AUTHOR
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Ryan Propper (rpropper(AT)stanford.edu), Dec 11 2004
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EXTENSIONS
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More terms from Daniel Hirschberg (dan(AT)ics.uci.edu), May 05 2007
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