A175948 Let @ denote binary concatenation. Then a(n) = A175945(n)@A175946(n).

1, 2, 3, 4, 5, 6, 7, 8, 11, 10, 9, 12, 13, 14, 15, 16, 23, 22, 19, 20, 21, 18, 17, 24, 27, 26, 25, 28, 29, 30, 31, 32, 47, 46, 39, 44, 41, 38, 35, 40, 43, 42, 45, 36, 37, 34, 33, 48, 55, 54, 51, 52, 53, 50, 49, 56, 59, 58, 57, 60, 61, 62, 63, 64, 95, 94, 79, 92, 81, 78, 71, 88

Offset: 1

Author

Dylan Hamilton, Oct 28 2010

Keywords

• base
• nonn

Comments

Apparently this means: take the run lengths of the 1's, then the run lengths of the 0's in the binary representation of n (scanned MSB to LSB), concatenate both lists and interpret the long list as a list of run length of alternatingly 1's and 0's. Example: n = 9 = 8+1 is 1001 in binary. Run lengths of 1's are 11 (two runs each of length 1). Run lengths of 0's are 2 (one run of length 2). The concatenation is 112, which is interpreted as 1 one, 1 zero, 2 ones, binary 1011, and recoded to decimal as a(9) = 8+2+1=11. [R. J. Mathar, Dec 07 2010]

Programs

Mathematica

takelist[l_, t_] := Module[{lent, term},Set[lent, Length[t]]; Table[l[[t[[y]]]], {y, 1, lent}]]
frombinrep[x_] := FromDigits[Flatten[Table[Table[If[OddQ[n], 1, 0], {d, 1, x[[n]]}], {n, 1, Length[x]}]], 2]
binrep[x_] := repcount[IntegerDigits[x, 2]]
onebinrep[x_]:=Module[{b},b=binrep[x];takelist[b,Range[1,Length[b],2]]]
zerobinrep[x_]:=Module[{b},b=binrep[x];takelist[b,Range[2,Length[b],2]]]
Table[frombinrep[Flatten[{onebinrep[n], zerobinrep[n]}]], {n,START,END}]