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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 * A031670 A031580 A028543

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 January 22 08:47 EST 2018. Contains 298042 sequences.