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A228158
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Numbers n such that the cardinality of (natural numbers <=n with a first digit of 1) = n/2.
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0
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2, 16, 22, 176, 222, 1776, 2222, 17776, 22222, 177776, 222222, 1777776, 2222222, 17777776, 22222222, 177777776, 222222222, 1777777776, 2222222222, 17777777776, 22222222222, 177777777776, 222222222222, 1777777777776, 2222222222222, 17777777777776
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OFFSET
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1,1
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COMMENTS
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This is conceptually related to Benford's law.
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LINKS
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FORMULA
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a(n) for odd values of n is simply "2" repeated (n+1)/2 times (sum as i=1->(n/2) of 10^(i-1)). For even values of n, it's a(n-1)*8.
G.f.: 2*(1+8*x)/((1-x)*(1+x)*(1-10*x^2)). [Joerg Arndt, Aug 14 2013]
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PROG
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(PARI) Vec(2*(1+8*x)/((1-x)*(1+x)*(1-10*x^2))+O(x^66)) \\ Joerg Arndt, Aug 14 2013
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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STATUS
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approved
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