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 A237041 Numbers n such that their 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 n. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS There are exactly 96 terms in this sequence smaller than 10^9. There are possibly an infinite number of these numbers. REFERENCES Andreas Boe, The Wasp Nest, Amazon Books, 2013 LINKS Andreas Boe and Giovanni Resta, Table of n, a(n) for n = 1..2838 (terms < 1.3*10^11, 92 terms from Andreas Boe) Andreas Boe, Boe Numbers Giovanni Resta, Decompositions for terms < 1.3*10^11 EXAMPLE 6724 -> 6.72.4 -> 110.1001000.100 -> 1101001000100 -> 6724. MATHEMATICA 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 *) CROSSREFS Sequence in context: A190292 A164972 A190129 * A031580 A028543 A145320 Adjacent sequences:  A237038 A237039 A237040 * A237042 A237043 A237044 KEYWORD nonn,base AUTHOR Andreas Boe, Feb 02 2014 STATUS approved

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Last modified June 18 07:06 EDT 2019. Contains 324203 sequences. (Running on oeis4.)