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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. 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.
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
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
KEYWORD
nonn,base
AUTHOR
Andreas Boe, Feb 02 2014
STATUS
approved

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Last modified April 23 18:16 EDT 2024. Contains 371916 sequences. (Running on oeis4.)