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%I #40 Aug 20 2014 13:37:28
%S 3,6,12,19,38,42,68,243,384,515,740,1709,5151,11049,45641,94729,
%T 185610,644593,726681,2296396,3098358,6178778,15743325,22436908,
%U 80141430,84300971,127495932,177416979,198423144,275354607
%N Indices of positive Fibonacci numbers whose binary expansions have record numbers of consecutive zeros.
%C 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
%H Peter Polm, <a href="http://bigintegers.blogspot.de/2013/02/a218076-three-more-with-c-on-64-bits.html">A218076 three more with C on 64 bits Linux</a> (BigInteger Algorithms blog).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FibonacciNumber.html">Fibonacci Number</a>
%e The first four records occur at 3, 6, 12, and 19:
%e F(3) = 10_2 (one zero),
%e F(6) = 1000_2 (three zeros),
%e F(12) = 10010000_2 (four zeros), and
%e F(19) = 1000001010101_2 (five zeros).
%e For the n=6178778, F(6178778) has 43 consecutive zeros.
%Y Cf. A059016, A087117.
%K base,nonn
%O 1,1
%A _Peter Polm_, Oct 20 2012
%E More terms from _Peter Polm_'s web site, _Joerg Arndt_, Aug 18 2014
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