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A218076
Indices of positive Fibonacci numbers whose binary expansions have record numbers of consecutive zeros.
1
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
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
Sequence in context: A209489 A181962 A226220 * A308722 A320192 A160732
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