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A237041
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Numbers k whose decimal expansion can be split into at least two parts whose binary equivalents can be concatenated (in the same order) to form the binary expansion of the original number k.
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1
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6724, 6725, 6726, 6727, 7844, 7845, 7846, 7847, 8964, 8965, 8966, 8967, 12832, 12833, 12834, 12835, 12836, 12837, 12838, 12839, 12840, 12841, 12842, 12843, 12844, 12845, 12846, 12847, 12848, 12849, 12850, 12851, 12852, 12853, 12854, 12855, 12856, 12857, 12858
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OFFSET
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1,1
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COMMENTS
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There are exactly 96 terms in this sequence smaller than 10^9.
This sequence may be infinite.
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REFERENCES
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Andreas Boe, The Wasp Nest, Amazon Books, 2013.
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LINKS
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EXAMPLE
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6724 -> 6.72.4 -> 110.1001000.100 -> 1101001000100 -> 6724.
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MATHEMATICA
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okQ[t_, d_, b_] := Catch[Block[{pw = 10, bL, y, r}, d == b && d < t && Throw@True; d < 10 && Throw@False; While[d > pw, y = Mod[d, pw]; bL = 2^If[y == 0, 1, IntegerLength[y, 2]]; Mod[b, bL] == y && okQ[t, Floor[d/pw], Floor[b/bL]] && Throw@True; pw *= 10]; False]]; okQ[n_] := okQ[n, n, n]; Select[Range[9, 15000], okQ] (* Giovanni Resta, Feb 03 2014 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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