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A222757
Irregular table of conjectured indices of Fibonacci numbers with exactly n 0-bits in their binary representation.
5
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
0,2
COMMENTS
Every nonnegative integer appears.
EXAMPLE
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}
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 *)
CROSSREFS
Cf. A004685 (Fibonacci numbers in binary), A222601, A222602, A222758.
Sequence in context: A020822 A197514 A112635 * A004568 A079904 A175630
KEYWORD
nonn,tabf
AUTHOR
T. D. Noe, Mar 11 2013
STATUS
approved