A222757 Irregular table of conjectured indices of Fibonacci numbers with exactly n 0-bits in their binary representation.

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, 26, 28, 33, 24, 31, 46, 25, 34, 37, 40, 41, 30, 36, 44, 32, 35, 43, 39, 42, 49, 38, 45, 50, 55, 58, 62, 56, 51, 52, 47, 53, 65, 59, 63, 67, 48, 54, 57, 61, 73

Offset: 0

Author

T. D. Noe, Mar 11 2013

Keywords

• nonn
• tabf

Comments

Every nonnegative integer appears.

Examples

			The irregular table begins
{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, 26, 28},
{33},
{24, 31, 46},
{25, 34, 37, 40, 41}
		

Links

• T. D. Noe, Rows n = 0..1000 of irregular triangle, flattened

Crossrefs

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

Programs

Mathematica

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}]
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 *)