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A385891 The number k = a(n) whose Stolarsky representation (row k of A385888) is the binary expansion of n (row n of A030302). Inverse Stolarsky representation of binary expansion of n.

%I A385891 #8 Jul 24 2025 10:52:15
%S A385891 1,2,4,3,9,6,7,5,22,15,14,10,17,11,12,8,56,36,38,24,35,23,25,16,43,28,
%T A385891 27,18,30,19,20,13,145,91,93,58,98,61,62,39,90,57,59,37,64,40,41,26,
%U A385891 111,70,72,45,69,44,46,29,77,49,48,31,51,32,33,21,378,235,237
%N A385891 The number k = a(n) whose Stolarsky representation (row k of A385888) is the binary expansion of n (row n of A030302). Inverse Stolarsky representation of binary expansion of n.
%C A385891 A permutation of the positive integers.
%H A385891 Casey Mongoven, <a href="/A200648/a200648.txt">Description of Stolarsky Representations</a>.
%F A385891 A385888(a(n)) = A030302(n).
%t A385891 nn=30;
%t A385891 stol[n_]:=stol[n]=If[n==1,{},If[n!=Round[Round[n/GoldenRatio]*GoldenRatio],Join[stol[Floor[n/GoldenRatio^2]+1],{0}],Join[stol[Round[n/GoldenRatio]],{1}]]];
%t A385891 ss=Table[stol[n],{n,nn}];
%t A385891 mnrm[s_]:=If[Min@@s==1,mnrm[DeleteCases[s-1,0]]+1,0];
%t A385891 Table[Position[ss,If[n==0,{},IntegerDigits[n,2]]][[1,1]],{n,0,mnrm[FromDigits[#,2]&/@ss+1]-1}]
%Y A385891 A000120 counts 1's in binary expansion, zeros A023416.
%Y A385891 A030302 gives binary expansion.
%Y A385891 A035506 is the Stolarsky array.
%Y A385891 A385888 is the Stolarsky representation, lengths A200648, sums A200649, zeros A200650, ranks A200714.
%Y A385891 Cf. A000045, A044813, A135818, A200651, A245563, A384890, A385886.
%K A385891 nonn
%O A385891 0,2
%A A385891 _Gus Wiseman_, Jul 24 2025