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Search: id:A054465
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| A054465 |
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Numbers n such that sum(k=1,n,d(k)) is an integer where d(k) is the decimal fraction 0.2k (e.g. d(14)=0.28). |
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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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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 ceil(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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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}] (Propper)
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CROSSREFS
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Sequence in context: A053400 A120599 A012797 this_sequence A118713 A132511 A012841
Adjacent sequences: A054462 A054463 A054464 this_sequence A054466 A054467 A054468
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KEYWORD
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base,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 30 2003
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EXTENSIONS
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More terms from Ryan Propper (rpropper(AT)stanford.edu), Jul 30 2005
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 06 2007
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