A272886 Number of distinct Fibonacci numbers among the contiguous substrings of the binary digits of n.

1, 3, 2, 3, 4, 4, 2, 4, 3, 4, 5, 4, 6, 4, 2, 4, 4, 3, 4, 4, 5, 5, 5, 5, 4, 6, 6, 4, 6, 4, 2, 4, 4, 5, 5, 3, 4, 4, 4, 5, 4, 5, 6, 5, 6, 5, 5, 5, 5, 4, 4, 6, 7, 6, 7, 5, 4, 6, 6, 4, 6, 4, 2, 4, 4, 4, 5, 5, 6, 5, 5, 4, 3, 4, 5, 4, 6, 4, 4, 5, 5, 4, 5, 5, 5, 6, 6, 6, 6, 6, 6, 5, 6, 5, 5, 5

Offset: 1

Author

Marko Riedel, May 08 2016

Keywords

• nonn

Examples

			a(53) = 7 because 53=(110101)_2 which contains (0)_2 = 0, (1)_2 = 1, (10)_2 = 2, (11)_2 = 3, (101)_2 = 5, (1101)_2 = 13 and (10101)_2 = 21. The one digit only contributes once as do two and zero.
		

Links

• Marko Riedel, Maple program to compute sequence.

Crossrefs

Cf. A000045, A078822, A272851, A272852.