A222757 - OEIS

%I #6 Mar 17 2024 16:16:55

%S 1,2,4,0,3,5,7,10,8,16,6,11,13,14,9,17,23,20,12,15,22,27,29,18,19,21,

%T 26,28,33,24,31,46,25,34,37,40,41,30,36,44,32,35,43,39,42,49,38,45,50,

%U 55,58,62,56,51,52,47,53,65,59,63,67,48,54,57,61,73

%N Irregular table of conjectured indices of Fibonacci numbers with exactly n 0-bits in their binary representation.

%C Every nonnegative integer appears.

%H T. D. Noe, <a href="/A222757/b222757.txt">Rows n = 0..1000 of irregular triangle, flattened</a>

%e The irregular table begins

%e {1, 2, 4},

%e {0, 3, 5, 7, 10},

%e {8, 16},

%e {6, 11, 13, 14},

%e {9, 17, 23},

%e {20},

%e {12, 15},

%e {22, 27, 29},

%e {18, 19, 21, 26, 28},

%e {33},

%e {24, 31, 46},

%e {25, 34, 37, 40, 41}

%t nn = 100; f = Fibonacci[Range[0, nn]]; t2 = Transpose[{Range[0, nn], f}]; Table[Select[Range[nn + 1], Count[IntegerDigits[t2[[#, 2]], 2], 0] == n &] - 1, {n, 0, nn/5}]

%t Insert[Flatten[Module[{nn=100,dc},dc=DigitCount[Fibonacci[Range[nn]],2,0];Table[Position[dc,n],{n,0,30}]]],0,4] (* _Harvey P. Dale_, Mar 17 2024 *)

%Y Cf. A004685 (Fibonacci numbers in binary), A222601, A222602, A222758.

%K nonn,tabf

%O 0,2

%A _T. D. Noe_, Mar 11 2013