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.

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, 27, 18, 30, 19, 20, 13, 145, 91, 93, 58, 98, 61, 62, 39, 90, 57, 59, 37, 64, 40, 41, 26, 111, 70, 72, 45, 69, 44, 46, 29, 77, 49, 48, 31, 51, 32, 33, 21, 378, 235, 237

Offset: 0

Author

Gus Wiseman, Jul 24 2025

Keywords

• nonn

Comments

A permutation of the positive integers.

Links

• Casey Mongoven, Description of Stolarsky Representations.

Crossrefs

A000120 counts 1's in binary expansion, zeros A023416.

A030302 gives binary expansion.

A035506 is the Stolarsky array.

A385888 is the Stolarsky representation, lengths A200648, sums A200649, zeros A200650, ranks A200714.

Cf. A000045, A044813, A135818, A200651, A245563, A384890, A385886.

Programs

Mathematica

nn=30;
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}]]];
ss=Table[stol[n],{n,nn}];
mnrm[s_]:=If[Min@@s==1,mnrm[DeleteCases[s-1,0]]+1,0];
Table[Position[ss,If[n==0,{},IntegerDigits[n,2]]][[1,1]],{n,0,mnrm[FromDigits[#,2]&/@ss+1]-1}]

Formula

A385888(a(n)) = A030302(n).