cp's OEIS Frontend

A175945 Start with the binary expansion of n; list the lengths of the runs of ones and interpret this list as lengths of runs of alternating ones and zeros in binary.

%I A175945 #10 Aug 02 2013 14:44:35
%S A175945 1,1,3,1,2,3,7,1,2,2,4,3,6,7,15,1,2,2,4,2,5,4,8,3,6,6,12,7,14,15,31,1,
%T A175945 2,2,4,2,5,4,8,2,5,5,11,4,9,8,16,3,6,6,12,6,13,12,24,7,14,14,28,15,30,
%U A175945 31,63,1,2,2,4,2,5,4,8,2,5,5,11,4,9,8,16,2,5,5,11,5,10,11,23,4,9,9,19,8,17
%N A175945 Start with the binary expansion of n; list the lengths of the runs of ones and interpret this list as lengths of runs of alternating ones and zeros in binary.
%C A175945 Trailing binary zeros don't affect the run lengths of 1's, so a(2n)=a(n). Trailing isolated binary ones add a run of a single 1, so a(4n+1) = 2*a(n) if a(n) is odd, a(4n+1) = 2*a(n)+1 if a(n) is even. - _R. J. Mathar_, Dec 07 2010
%H A175945 Paul Tek, <a href="/A175945/b175945.txt">Table of n, a(n) for n = 1..10000</a>
%e A175945 n=43 in binary is 101011, where the 1 has run-lengths of 1, 1 and 2. This is interpreted as a run of 1 one, run of 1 zero and run of 2 one's, 1011, which back to decimal is a(43)=11. - _R. J. Mathar_, Dec 07 2010
%t A175945 takelist[l_, t_] := Module[{lent, term},Set[lent, Length[t]]; Table[l[[t[[y]]]], {y, 1, lent}]]
%t A175945 frombinrep[x_] := FromDigits[Flatten[Table[Table[If[OddQ[n], 1, 0], {d, 1, x[[n]]}], {n, 1, Length[x]}]], 2]
%t A175945 binrep[x_] := repcount[IntegerDigits[x, 2]]
%t A175945 onebinrep[x_]:=Module[{b},b=binrep[x];takelist[b,Range[1,Length[b],2]]]
%t A175945 zerobinrep[x_]:=Module[{b},b=binrep[x];takelist[b,Range[2,Length[b],2]]]
%t A175945 Table[frombinrep[onebinrep[n]], {n,START,END}]
%K A175945 base,easy,nonn
%O A175945 1,3
%A A175945 _Dylan Hamilton_, Oct 28 2010
%E A175945 Definition rewritten by _N. J. A. Sloane_, Dec 08 2010.