A218076 Indices of positive Fibonacci numbers whose binary expansions have record numbers of consecutive zeros.

3, 6, 12, 19, 38, 42, 68, 243, 384, 515, 740, 1709, 5151, 11049, 45641, 94729, 185610, 644593, 726681, 2296396, 3098358, 6178778, 15743325, 22436908, 80141430, 84300971, 127495932, 177416979, 198423144, 275354607

Offset: 1

Author

Peter Polm, Oct 20 2012

Keywords

• base
• nonn

Comments

Positions of records in the auxiliary sequence 0, 0, 0, 1, 0, 1, 3, 1, 1, 3, 1, 2, 4, 2, 2, 3, 1, 3, 4, 5, 2,... = A087117(Fibonacci(n)). - R. J. Mathar, Nov 05 2012

Examples

			The first four records occur at 3, 6, 12, and 19:
F(3) = 10_2 (one zero),
F(6) = 1000_2 (three zeros),
F(12) = 10010000_2 (four zeros), and
F(19) = 1000001010101_2 (five zeros).
For the n=6178778, F(6178778) has 43 consecutive zeros.
		

Links

• Peter Polm, A218076 three more with C on 64 bits Linux (BigInteger Algorithms blog).
• Eric Weisstein's World of Mathematics, Fibonacci Number

Crossrefs

Cf. A059016, A087117.

Extensions

More terms from Peter Polm's web site, Joerg Arndt, Aug 18 2014