A218076 - OEIS

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

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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