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

1,1

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

Links

Table of n, a(n) for n=1..30.

Peter Polm, A218076 three more with C on 64 bits Linux (BigInteger Algorithms blog).

Eric Weisstein's World of Mathematics, Fibonacci Number

Example

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.

Crossrefs

Cf. A059016, A087117.

Sequence in context: A209489 A181962 A226220 * A308722 A320192 A160732

Adjacent sequences: A218073 A218074 A218075 * A218077 A218078 A218079

Keyword

base,nonn

Author

Peter Polm, Oct 20 2012

Extensions

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

Status

approved