A237041 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.

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

Offset

1,1

Comments

There are exactly 96 terms in this sequence smaller than 10^9.

This sequence may be infinite.

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: A190129 A345581 A345838 * A031580 A028543 A145320

Adjacent sequences: A237038 A237039 A237040 * A237042 A237043 A237044

Keyword

nonn,base

Author

Andreas Boe, Feb 02 2014

Status

approved