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Irregular table of conjectured indices of Fibonacci numbers with exactly n 1-bits in their binary representation.
5

%I #4 Mar 11 2013 14:20:51

%S 0,1,2,3,6,4,5,9,12,7,8,11,15,18,10,13,19,14,21,24,25,17,16,20,22,30,

%T 26,32,38,23,27,28,31,35,29,34,36,39,48,33,47,37,42,45,68,40,43,54,57,

%U 60,41,51,52,53,44,49,50,61,66,59,64,46,56,55,71,77

%N Irregular table of conjectured indices of Fibonacci numbers with exactly n 1-bits in their binary representation.

%C Every nonnegative integer appears.

%H T. D. Noe, <a href="/A222758/b222758.txt">Rows n = 0..1000 of irregular triangle, flattened</a>

%e The irregular table begins

%e {0},

%e {1, 2, 3, 6},

%e {4, 5, 9, 12},

%e {7, 8},

%e {11, 15, 18},

%e {10, 13, 19},

%e {14, 21, 24, 25},

%e {17},

%e {16, 20, 22, 30},

%e {26, 32},

%e {38},

%e {23, 27, 28, 31, 35}

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

%Y Cf. A004685 (Fibonacci numbers in binary), A222601, A222602, A222757.

%K nonn,tabf

%O 0,3

%A _T. D. Noe_, Mar 11 2013