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A054465
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Numbers k such that Sum_{j=1..k} d(j) is an integer where d(j) is the decimal fraction 0.2j (e.g., d(14) = 0.28).
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0
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4, 20, 349, 474, 3999, 4624, 5000, 35624, 390624, 499999, 1609375, 27109375, 40000000, 137109375, 149999999, 3000000000, 4787109375, 6787109375, 24999999999, 200000000000, 281787109375, 1581787109375, 3499999999999
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OFFSET
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1,1
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COMMENTS
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Conjecture: the number of k > 0 such that a(k) <= n is asymptotic to C*log(n), C > 0.
Also, solutions x to the quadratic modular equation: x^2 + x + c ==0 (mod 10^a) where c = ((8-18*a)*10^a + 10^(2*a))/40, such that ceiling(10^(a-1)/2) <= x <= (10^a/2)-1, a=1,2,... - Herman Jamke (hermanjamke(AT)fastmail.fm), May 06 2007
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LINKS
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EXAMPLE
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0.2 + 0.4 + 0.6 + 0.8 = 2, hence 4 is in the sequence.
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MATHEMATICA
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s = 0; Do[s += (2*n)/10^Length[IntegerDigits[2*n]]; If[IntegerQ[s], Print[n]], {n, 1, 10^6}] (* Ryan Propper, Jul 30 2005 *)
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 06 2007
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STATUS
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approved
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