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Periodic vertical binary vectors of Fibonacci numbers, topmost bits being most significant.
3

%I #7 Mar 31 2012 14:02:29

%S 3,6,90,202474,802914372650,124876754670311211270396330,

%T 2261740218128437766312179308277308483058208661638110890,

%U 7527129205899945471753233641719262207829849606092782843679109711117799287001392666047916596823438974998183293610

%N Periodic vertical binary vectors of Fibonacci numbers, topmost bits being most significant.

%H A. Karttunen, <a href="/A036286/b036286.txt">Table of n, a(n) for n = 0..10</a>

%H A. Karttunen, <a href="/A036284/a036284.c.txt">C program for computing this sequence</a>

%F a(n) = Sum_{k=0..A007283(n)-1} ([A000045((A007283(n)-1)-k)/(2^n)] mod 2) * 2^k, where [] stands for floor function.

%e When Fibonacci numbers are written in binary (see A004685), under each other as:

%e 0000000 (0)

%e 0000001 (1)

%e 0000001 (1)

%e 0000010 (2)

%e 0000011 (3)

%e 0000101 (5)

%e 0001000 (8)

%e 0001101 (13)

%e 0010101 (21)

%e 0100010 (34)

%e 0110111 (55)

%e 1011001 (89)

%e it can be seen that the bits in the n-th column from right repeat after the period of A007283(n): 3, 6, 12, 24, ... (see also A001175). This sequence is formed from those bits: 011, binary for 3, thus a(0) = 3. 000110, binary for 6, thus a(1) = 6, 000001011010, binary for 90, thus a(2) = 90. Cf. A036284.

%Y See comments at A036284. a(n)/A036287(n) can be interpreted as fractions.

%K nonn,base

%O 0,1

%A _Antti Karttunen_, Nov 01 1998. Entry revised Dec 29 2007.